A359395 Least odd prime p in position n in the prime factorization of M(p) = 2^(p - 1) - 1.

3, 5, 17, 13, 71, 37, 157, 61, 211, 313, 1289, 241, 337, 181, 577, 601, 541, 1381, 421, 1201, 1009, 1621, 1873, 3433, 4561, 1801, 3301, 2161, 3061, 5281, 3361, 2521, 7393, 6481, 4201, 4621, 8737, 9181, 6301, 19501, 7561, 16633, 12241, 26881, 15601, 9241, 21001, 14281, 12601, 53551

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Carlos Rivera, Puzzle 1116. A358527, The Prime Puzzles & Problems Connection.

Example

M(5) = 15 = 3*5 and 5 is in second position in the prime factorization of M(5), and no lesser odd prime satisfies this, so a(2) = 5.
M(17) = 65535 = 3*5*17*257 and 17 is in third position in the prime factorization of M(17), and no lesser odd prime satisfies this, so a(3) = 17.

Mathematica

f[n_] := Module[{p = Prime[n]}, Count[Prime[Range[n - 1]], _?(PowerMod[2, p - 1, #] == 1 &)] + 1]; f[1] = 0; With[{s = Array[f, 4000]}, ind = TakeWhile[ FirstPosition[s, #] & /@ Range[Max[s]] // Flatten, NumberQ ]; Prime[ind]] (* Amiram Eldar, Jan 02 2023 *)

Prog

(PARI) isok(p, n) = my(f=factor(2^(p-1) - 1, p+1)); if (#f~ < n, 0, f[n, 1] == p);
a(n) = my(p=3); while(!isok(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Jan 13 2023

Crossrefs

Cf. A098102, A358527.

Sequence in context: A158895 A085418 A339944 * A292008 A139427 A360802

Adjacent sequences: A359392 A359393 A359394 * A359396 A359397 A359398

Keyword

nonn

Author

Jean-Marc Rebert, Dec 31 2022

Status

approved