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%I #18 Mar 14 2019 09:35:03
%S 271129,271577,482719,575041,603713,903983,965431,1518781,1624097,
%T 1639459,2131043,2131099,2541601,2931767,2931991,3083723,3098059,
%U 3555593,3608251,4067003,4573999,6134663,6135559,6557843,6676921,6678713,6742487,6799831,7400371,7523267,7523281,7761437,7765021,7892569,8007257,8629967,8840599,8871323,9208337,9454129,9454157,9854491,9854603,9930469,9937637,10192733,10422109,10675607
%N Odd integers m such that for every integer k > 0, m*2^k+1 has a divisor in the set {3, 5, 7, 13, 17, 241}.
%C For n > 48, a(n) = a(n-48) + 11184810; the first 48 values are in the data.
%C The set {3, 5, 7, 13, 17, 241} is the set of prime divisors of 2^24 - 1. Hence for every p in the set the multiplicative order of 2 modulo p divides 24. Note that twice the product of {3, 5, 7, 13, 17, 241} is 11184810. - _Jeppe Stig Nielsen_, Mar 10 2019
%C Subset of provable Sierpiński numbers A076336. - _Jeppe Stig Nielsen_, Mar 10 2019
%F For n > 48, a(n) = a(n-48) + 11184810.
%o (PARI) D=[3, 5, 7, 13, 17, 241];P=2*lcm(D);M=lcm(apply(d->znorder(Mod(2,d)),D));forstep(k=1,+oo,2,if(k%P==1,print();print());for(n=0,M-1,for(i=1,#D,k*Mod(2,D[i])^n+1==0 && next(2));next(2));print1(k,", ")) \\ _Jeppe Stig Nielsen_, Mar 10 2019
%Y Cf. A076336, A244070, A244071, A244072, A244073, A244074, A244076.
%K nonn
%O 1,1
%A _Pierre CAMI_, Jun 30 2014
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