cp's OEIS Frontend

A250209 a(n) = least k such that k * n is in A072226, or 0 if no such k exists.

%I A250209 #63 Jul 14 2025 22:52:16
%S A250209 2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,5,1,2,2,1,2,1,6,1,1,2,5,1,1,1,1,1,
%T A250209 8,34,8,1,2,1,10,1,2,350,2,1,111,4,1,3,16,4,15,28,3,1,206,3,10,2,1,1,
%U A250209 2,3,1,15,637,12,1,4,22,17,104,4,2,1012,1,1
%N A250209 a(n) = least k such that k * n is in A072226, or 0 if no such k exists.
%C A250209 Conjecture: a(n) > 0 for all n.
%C A250209 a(n) is currently unknown for n = 121, 124, 143, 162, 171, 172, 185, 188, 197, 215, ..., for which we have n * a(n) > 130000.
%C A250209 a(121) = (A117545(2048))/11 and they are both currently unknown.
%C A250209 A117545(2^n) = a(A064549(n)).
%C A250209 a(130) = 917, a(144) = 820, a(164) = 720, a(201) = 606. - _Max Alekseyev_, Dec 04 2024
%H A250209 Eric Chen, <a href="/A250209/b250209.txt">Table of n, a(n) for n = 1..120</a>
%H A250209 Eric Chen, <a href="/A250209/a250209_1.txt">Table of n, a(n) for n = 1..300 status</a>
%t A250209 Table[k=1; While[!PrimeQ[Cyclotomic[n*k, 2]], k++]; k, {n, 43}]
%o A250209 (PARI) a(n) = {k = 1; while (!isprime(polcyclo(k*n, 2)), k++); k;} \\ _Michel Marcus_, Jan 18 2015
%K A250209 nonn
%O A250209 1,1
%A A250209 _Eric Chen_, Jan 18 2015