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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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?

LINKS

Table of n, a(n) for n=1..66.

Jonas Kaiser, On the relationship between the Collatz conjecture and Mersenne prime numbers, arXiv:1608.00862 [math.GM], 2016.

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

Cf. A001917, A001567.

Sequence in context: A298138 A071788 A220133 * A298258 A298929 A118497

Adjacent sequences:  A300098 A300099 A300100 * A300102 A300103 A300104

KEYWORD

nonn

AUTHOR

Jonas Kaiser, Feb 24 2018

STATUS

approved

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Last modified October 22 12:48 EDT 2021. Contains 348168 sequences. (Running on oeis4.)