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A337818 Odd integers k>=3 such that k*(k-1)/2 divides 2^((k-1)/2)+1. 9

%I #40 Oct 07 2020 05:44:53

%S 3,19,163,1459,370387,6381667,30001267,40417219,42384547,42633379,

%T 86093443,190008019,268435459,634471219,1630068787,2415919123,

%U 3103616899,4677743683,7734924739,7920392707,8114552947,10323768979,13086951139,13984274323,18839387107,19764019603,36164859427

%N Odd integers k>=3 such that k*(k-1)/2 divides 2^((k-1)/2)+1.

%C Computed terms are prime. Is it always the case? If not it would be interesting to compute the pseudoprimes.

%C Conjecture: a(n) == 1 mod 162 for n >= 6. The next few larger terms of the form 162*k+1 are: 44165935747, 46696027123, 85683674179, 88567070707, 101297654083, 131264938963, 131315541283, 177876176419, 195689448883, 196838306227, 213339588643, 310256425603, 378897238243, 502106519683, 588454831747, 611537689459, 641551809187, 735075731107, 745956214867, 755236606483, 771153067603, 872146803043 (and they are all primes). - _Chai Wah Wu_, Oct 06 2020

%t Select[Range[3, 400000, 2], PowerMod[2, (# - 1)/2, (t = #*(# - 1)/2)] == t - 1 &] (* _Amiram Eldar_, Sep 23 2020 *)

%o (PARI) is(n) = n%2 && n>=3 && Mod(2, n*(n-1)/2)^((n-1)/2) == -1 \\ _David A. Corneth_, Sep 23 2020

%K nonn

%O 1,1

%A _Benoit Cloitre_, Sep 23 2020

%E a(7)-a(27) from _Amiram Eldar_, Sep 23 2020

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)