Prime Runs
(concatenated)
On Fri, Nov 19, 2010
at 11:36 AM, Eric Angelini wrote:
> Hello SeqFans,
>
> Here is P:
>
> P is a permutation of the
Naturals (by definition) and
> P self-describes its own prime
runs’ sizes of concatenated terms:
>
> P =
2,3,1,4,23,5,6,7,8,19,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27,28,29,30,31,32,X,...
>
> -concatenating
the first 2 terms produces a prime --> 2+3 = ‘23’
> -concatenating
the next 3 terms produces a prime --> 1+4+23
= ‘1423’
> -concatenating
the next 1 term produces a prime --> ‘5’
> -concatenating
the next 4 terms produces a prime -->
6+7+8+19 = ‘67819’
> -concatenating
the next 23 terms produces a prime --> but which one?
>
> ... I’m not sure
that the term X (after 32), is computable...
>
> As always,
"in building this sequence, always use the smallest available
> integer not
leading to a contradiction"...
>
> Best,
> É.
__________
[Maximilian
Hasler]
With my little program
I get the values listed below. I only put the first 100 with explanation, and
then 400 more. The term 581 which follows 309 leads to a quite large prime
(over 400 digits, I think it corresponds to the a(19)=139
concatenated terms) but all other (even many following) primes are relatively
small.
{a=[2];
remain=1; pointer=1; print1(prefix="2");
for(n=1,499, my(used=Set(a));
if( !remain,
remain=a[pointer++];
print1(" /*
prime=",prefix," */"); prefix="";
);
for(i=1,1e9, setsearch(used,i) & next;
remain >1| ispseudoprime(
eval( Str( prefix,i ))) | next;
prefix=Str(prefix,i); a=concat(a,i); print1(",
"i); remain--; break
); /* end for i */
);a}
2, 3 [prime=23], 1, 4, 9
[prime=149], 5 [prime=5], 6, 7, 8, 19 [prime=67819], 10, 11, 12, 13, 14, 15, 16,
17, 139 [prime=1011121314151617139], 18, 20, 21, 22, 59 [prime=1820212259], 23,
24, 25, 26, 27, 63 [prime=232425262763], 28, 29, 30, 31, 32, 33, 71
[prime=28293031323371], 34, 35, 36, 37, 38, 39, 40, 57
[prime=3435363738394057], 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
54, 55, 56, 58, 60, 109 [prime=414243444546474849505152535455565860109], 61,
62, 64, 65, 66, 67, 68, 69, 70, 189 [prime=616264656667686970189], 72, 73, 74,
75, 76, 77, 78, 79, 80, 81, 179 [prime=72737475767778798081179], 82, 83, 84,
85, 86, 87, 88, 89, 90, 91, 92, 173 [prime=8283848586878889909192173], 93, 94,
95, ...
P(1..500) = [2, 3, 1, 4, 9,
5, 6, 7, 8, 19, 10, 11, 12, 13, 14, 15, 16, 17, 139, 18, 20, 21, 22, 59, 23,
24, 25, 26, 27, 63, 28, 29, 30, 31, 32, 33, 71, 34, 35, 36, 37, 38, 39, 40, 57,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 109,
61, 62, 64, 65, 66, 67, 68, 69, 70, 189, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 179, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 173, 93, 94, 95, 96, 97, 98,
99, 100, 101, 102, 103, 104, 121, 105, 106, 107, 108, 110, 111, 112, 113, 114,
115, 116, 117, 118, 223, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130,
131, 132, 133, 167, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146,
147, 148, 149, 213, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161,
162, 163, 164, 165, 737, 166, 168, 169, 170, 171, 172, 174, 175, 176, 177, 178,
180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196,
197, 198, 199, 200, 201, 202,203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
214, 215, 216, 217, 218, 219, 220, 221, 222, 224, 225, 226, 227, 228, 229, 230,
231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246,
247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262,
263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278,
279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294,
295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 581,
310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325,
326, 407, 327, 328, 329, 330, 331, 332, 333, 334,335, 336, 337, 338, 339, 340,
341, 342, 343, 344, 345, 373, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355,
356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 793, 366, 367, 368, 369, 370,
371, 372, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387,
759, 388, 389, 390, 391, 392, 393, 394, 395]
Merci Maximilian !
__________
Breaking news :
Maximilian a fait entrer cette
suite dans l’OEIS.
__________
à+
É.