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A345460 Odd numbers k with (k-1)/2 not prime such that p-1 | k-1 or k-1 | p-1 for every prime p | 2^(k-1)-1. 0
1, 3, 9, 13, 17, 19, 31, 33, 37, 43, 65, 79, 115, 129, 187, 223, 367, 403, 535, 763, 835 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Are there only finitely many such numbers? No more terms below 2217.

For those numbers k, if k <> 2^m + 1, then k == 1 (mod 6).

LINKS

Table of n, a(n) for n=1..21.

MATHEMATICA

q[k_] := AllTrue[FactorInteger[2^(k - 1) - 1][[;; , 1]], Divisible[k - 1, # - 1] || Divisible[# - 1, k - 1] &]; Select[Range[1, 230, 2], ! PrimeQ[(# - 1)/2] && q[#] &]

CROSSREFS

Cf. A334797 (see comments section).

Sequence in context: A063791 A077791 A176393 * A239320 A243656 A240108

Adjacent sequences:  A345457 A345458 A345459 * A345461 A345462 A345463

KEYWORD

nonn,more

AUTHOR

Amiram Eldar and Thomas Ordowski, Jun 20 2021

STATUS

approved

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Last modified October 24 10:03 EDT 2021. Contains 348225 sequences. (Running on oeis4.)