login
A300101
a(n) = (pp-1)/x, where pp = A001567(n) and x = ord(2,pp), the smallest positive integer such that 2^x == 1 (mod pp).
4
34, 14, 23, 46, 77, 48, 68, 186, 44, 75, 47, 117, 112, 273, 19, 312, 390, 10, 221, 160, 106, 45, 342, 42, 157, 64, 229, 237, 699, 345, 714, 352, 348, 668, 195, 285, 575, 487, 56, 163, 502, 9, 357, 439, 310, 296, 208, 803, 151, 684, 217, 2038, 324, 315, 1666, 344, 1973, 319, 607, 2763, 62, 1777, 1122, 1360, 1135, 2603
OFFSET
1,1
COMMENTS
For primes, this definition has a clear distribution over the natural numbers (see A001917), whereas there is no such distribution for pseudoprimes. Among the first 10^6 pseudoprimes of this sequence, the smallest number is 9. Are there any numbers in this sequence which are smaller than 9?
There is no value smaller than 9 for all the pseudoprimes below 2^64. - Amiram Eldar, Nov 09 2023
FORMULA
a(n) = (A001567(n) - 1) / A306413(n). - Jianing Song, Dec 12 2021
MATHEMATICA
((# - 1)/MultiplicativeOrder[2, #]) & /@ Select[Range[10^5], CompositeQ[#] && PowerMod[2, # - 1, #] == 1 &] (* Amiram Eldar, Nov 09 2023 *)
PROG
(PARI) is_A001567(n)={Mod(2, n)^n==2 & !isprime(n) & n>1};
lista(nn) = {for (n=1, nn, if (is_A001567(n), print1((n-1)/znorder(Mod(2, n)), ", "); ); ); } \\ Michel Marcus, Feb 25 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonas Kaiser, Feb 24 2018
STATUS
approved