(n+1) is not divisible by any digit of n

Hello SeqFans,

We want (n+1) not to be divisible by any digit of n [with (n+1) the smallest integer not yet present in the seq.]

S = 2, 3, 4, 5, 6, 7, 8, 9, 20, 23, 25, 27, 29, 33, 34, 35, 37, 38, 43, 46, 47, 50, 52, 53, ...

No integer with a "1" digit can enter S, of course, and all primes will appear -- except the ones containing a "1".

Best,

É.

__________

[Maximilian Hasler]:

Bonsoir Eric,

Je pense qu’une erreur s’est glissée dans tes calculs ; au lieu du 34 je trouve 22 :

EA(Nmax)={my(a=[],d=[0],u=0,nd); while( #a<Nmax, for( t=2,9e9, bittest(u,t) & next; for(i=1+!d[1],#d, t%d[i] || next(2)); nd=Set(digits(t)); setsearch(nd,1) & next; a=concat(a,t); u+=1<<t; d=nd; print1(t",");break));a}

EA(100) = 2, 3, 4, 5, 6, 7, 8, 9, 20, 23, 25, 27, 29, 33, 22, 35, 26, 37, 32, 43, 34, 38, 28, 39, 40, 30, 44, 42, 45, 46, 47, 50, 24, 49, 53, 52, 57, 36, 55, 48, 54, 58, 59, 56, 62, 63, 64, 65, 67, 68, 69, 70, 60, 73, 74, 66, 75, 72, 79, 76, 80, 77, 78, 82, 83, 85, 84, 86, 87, 89, 92, 93, 88, 90, 94, 95, 96, 97, 200, 99, 98, 202, 203, 205, 207, 209, 223, 227, 225, 229, 233, 235, 239, 245, 237, 247, 243, 253, 257, 249, ...

P.-S.

Il me semble que ta version correspond à "a(n+1)>a(n)" et non pas à "a(n+1) pas encore utilisé".

__________

Yes, Maximilian is right; the above S sequence is the one where we want "a(n+1)>a(n)" and not "(n+1) is the smallest integer not yet present in the seq." – which is exactly the one computed by Maximilian. [The monotonically increasing sequence is now https://oeis.org/A217491.]

Many thanks for the correction, Maximilian,

Best,

É.

__________

October 5th update

[Jean-Marc Falcoz]:

First 10.000 terms of EA(Nmax), computed by Jean-Marc Falcoz, and the subsequent graph (above); this is now https://oeis.org/A217489 :

{2, 3, 4, 5, 6, 7, 8, 9, 20, 23, 25, 27, 29, 33, 22, 35, 26, 37, 32, 43, 34, 38, 28, 39, 40, 30, 44, 42, 45, 46, 47, 50, 24, 49, 53, 52, 57, 36, 55, 48, 54, 58, 59, 56, 62, 63, 64, 65, 67, 68, 69, 70, 60, 73, 74, 66, 75, 72, 79, 76, 80, 77, 78, 82, 83, 85, 84, 86, 87, 89, 92, 93, 88, 90, 94, 95, 96, 97, 200, 99, 98, 202, 203, 205, 207, 209, 223, 227, 225, 229, 233, 235, 239, 245, 237, 247, 243, 253, 257, 249, 255, 259, 263, 265, 267, 269, 273, 275, 277, 279, 283, 287, 285, 289, 293, 295, 299, 303, 206, 297, 305, 208, 307, 220, 309, 224, 323, 325, 329, 335, 226, 327, 337, 230, 343, 238, 347, 242, 333, 232, 349, 250, 339, 236, 353, 244, 345, 254, 357, 248, 355, 256, 359, 262, 363, 260, 365, 266, 367, 268, 369, 272, 373, 274, 375, 278, 377, 284, 379, 286, 383, 290, 385, 292, 389, 298, 393, 280, 387, 302, 395, 296, 397, 304, 322, 403, 326, 407, 222, 399, 308, 332, 409, 246, 405, 234, 425, 423, 427, 429, 433, 334, 338, 340, 346, 350, 328, 437, 358, 356, 344, 362, 439, 370, 320, 443, 374, 382, 445, 258, 447, 270, 435, 386, 364, 394, 398, 380, 388, 404, 282, 449, 294, 453, 406, 422, 455, 306, 352, 457, 342, 463, 430, 434, 442, 459, 354, 446, 454, 366, 368, 428, 465, 458, 378, 436, 466, 467, 470, 330, 376, 400, 390, 392, 469, 473, 475, 402, 477, 426, 479, 438, 478, 450, 462, 483, 482, 485, 474, 486, 487, 489, 490, 493, 494, 497, 498, 499, 502, 503, 424, 495, 506, 448, 505, 204, 507, 228, 509, 264, 523, 527, 529, 533, 452, 537, 464, 525, 539, 472, 535, 476, 526, 543, 538, 484, 522, 547, 534, 542, 549, 546, 553, 488, 530, 496, 545, 554, 557, 276, 555, 252, 559, 336, 440, 550, 288, 563, 508, 324, 565, 524, 567, 536, 532, 569, 544, 558, 348, 562, 573, 548, 566, 556, 568, 572, 577, 372, 575, 384, 574, 578, 396, 460, 579, 408, 570, 432, 583, 586, 587, 444, 582, 589, 492, 593, 584, 594, 597, 456, 598, 564, 599, 528, 603, 500, 468, 585, 588, 596, 592, 607, 520, 609, 560, 602, 595, 552, 623, 605, 604, 590, 606, 580, 622, 625, 627, 629, 633, 608, 620, 635, 626, 637, 628, 639, 632, 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3275, 3277, 3287, 3289, 3283, 3293, 3295, 3299, 3305, 2224, 3207, 3307, 2228, 3225, 3323, 3325, 3329, 3335, 2234, 3337, 2230, 3343, 2242, 3237, 3347, 2246, 3243, 3349, 2254, 3249, 3353, 2236, 3355, 2248, 3255, 3359, 2252, 3267, 3365, 2258, 3273, 3373, 2260, 3279, 3377, 2264, 3285, 3367, 2266, 3297, 3379, 2270, 3303, 2240, 3309, 2272, 3327, 3383, 2276, 3333, 2278, 3345, 2282, 3339, 2284, 3357, 2288, 3363, 2290, 3369, 2294, 3385, 2302, 3389, 2300, 3395, 2296, 3387, 2306, 3397, 2308, 3403, 2326, 3407, 2330, 3409, 2338, 3425, 3427, 3433, 2342, 3437, 2350, 3439, 2354, 3443, 2362, 3445, 2366, 3449, 2374, 3455, 2378, 3457, 2386, 3463, 2390, 3467, 2398, 3469, 2402, 3375, 2332, 3473, 2426, 3393, 2320, 3475, 2434, 3479, 2438, 3485, 2422, 3399, 2324, 3487, 2446, 3405, 2458, 3423, 3493, 2450, 3429, 3497, 2462, 3435, 2474, 3447, 2470, 3453, 2482, 3459, 2486, 3465, 2494, 3477, 2498, 3489, 2506, 3483, 2522, 3499, 2530, 3503, 2336, 3505, 2344, 3509, 2348, 3523, 3527, 3529, 3533, 2356, 3539, 2368, 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[Hans Havermann]:

> No integer with a "1" digit can enter S (...)

Nor can any positive multiple of 2520.

Here's a graph of 54637 points:

Merci Jean-Marc, Maximilian et Hans !