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A328700 Numbers k dividing nonzero terms in A003095.

%I A328700 #13 Jul 21 2024 03:42:16
%S A328700 1,2,5,10,13,26,41,65,82,130,137,149,205,229,274,293,298,397,410,458,
%T A328700 509,533,586,661,677,685,709,745,761,794,809,877,881,1018,1066,1145,
%U A328700 1217,1249,1277,1322,1354,1370,1418,1465,1490,1522,1601,1618,1754,1762,1781,1937,1985,2053,2290
%N A328700 Numbers k dividing nonzero terms in A003095.
%C A328700 k is a term if and only if A328699(k) = 0, in which case all the indices m such that k divides A003095(m) are m = t*A248218(k), t = 0, 1, 2, 3, ...
%H A328700 Amiram Eldar, <a href="/A328700/b328700.txt">Table of n, a(n) for n = 1..1000</a>
%e A328700 41 divides A003095(7) = 210066388901, so 41 is in this sequence. In addition, 41 divides A003095(m) if and only if 7 divides m.
%e A328700 29 is not a term: {A003095(n) mod 29} = {0, 1, 2, 5, 26, 10, 14, 23, 8, 7, 21, 7, 21, 7, 21, ...}, so 29 does not divides A003095(m) for any m > 0.
%o A328700 (PARI) v(n) = my(v=[0],k,flag=1); for(i=2, n+1, k=(v[#v]^2+1)%n; v=concat(v, k); for(j=1, i-1, if(v[j]==k, flag=0)); if(flag==0, break())); v;
%o A328700 is(n) = !(v(n)[#v(n)]);
%Y A328700 Cf. A003095, A328699, A248218.
%Y A328700 The primes in this sequence are given by A247981.
%K A328700 nonn
%O A328700 1,2
%A A328700 _Jianing Song_, Oct 26 2019