This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350703 #32 Feb 16 2022 13:20:49
%S A350703 3,18,5,9,15,50,40,16,7,156,60,25,180,102,113,81,10,50,29,159,51,56,
%T A350703 24,36,47,90,337,72,55,106,33,102,780,28,117,25,155,540,60,104,223,
%U A350703 1012,168,180,91,540,3132,47,510,412,154,45,80,432,201,36,90,144,97,53,279,880
%N A350703 a(n) is the least integer k such that (2*n*k+1) | (2^k-1).
%C A350703 The formula 2nk+1 is used to find trivial factors of Mersenne(p). Here it is used for all exponents (prime exponents and not prime exponents).
%C A350703 Mersenne primes of A000043 can be found in this sequence too (except for 2). E.g.: a(1, 3, 9, 315, 3855, 13797) = A000043(2..7).
%C A350703 If n mod 4 = 2 then a(n) must be composite.
%H A350703 Karl-Heinz Hofmann, <a href="/A350703/b350703.txt">Table of n, a(n) for n = 1..10000</a>
%e A350703 a(5) = 15: 2^15 - 1 = 32767; 2*5*15 + 1 = 151; 32767 mod 151 = 0, and there are no numbers < 15 which satisfy the requirement for n = 5.
%t A350703 a[n_] := Module[{k = 1}, While[PowerMod[2, k, 2*n*k + 1] != 1, k++]; k]; Array[a, 62] (* _Amiram Eldar_, Feb 03 2022 *)
%o A350703 (Python)
%o A350703 def A350703(k,expo):
%o A350703 while pow(2, expo, 2*k*expo+1) != 1: expo += 1
%o A350703 return expo
%o A350703 print([A350703(k,1) for k in range(1, 63)])
%o A350703 (PARI) a(n) = my(k=1); while (Mod(2, 2*n*k+1)^k != 1, k++); k; \\ _Michel Marcus_, Feb 03 2022
%Y A350703 Cf. A000043, A002515, A188130, A122095, A188133, A350702.
%K A350703 nonn
%O A350703 1,1
%A A350703 _Karl-Heinz Hofmann_, Feb 03 2022