A244561 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}.

271129, 271577, 482719, 575041, 603713, 903983, 965431, 1518781, 1624097, 1639459, 2131043, 2131099, 2541601, 2931767, 2931991, 3083723, 3098059, 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

Offset: 1

Author

Pierre CAMI, Jun 30 2014

Keywords

• nonn

Comments

For n > 48, a(n) = a(n-48) + 11184810; the first 48 values are in the data.

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

Subset of provable Sierpiński numbers A076336. - Jeppe Stig Nielsen, Mar 10 2019

Crossrefs

Cf. A076336, A244070, A244071, A244072, A244073, A244074, A244076.

Programs

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

Formula

For n > 48, a(n) = a(n-48) + 11184810.