A265630 Numbers n > 1 such that 2^m == 1 (mod n^2), where m = A002326((n-1)/2).

1093, 3511, 7651, 10533, 14209, 17555, 22953, 31599, 42627, 45643, 52665, 99463, 136929, 157995, 228215, 298389, 410787, 684645, 2053935, 3837523, 11512569, 19187615, 26862661, 34537707, 49887799, 57562845, 80587983, 134313305, 149663397, 172688535, 241763949, 249438995, 349214593, 402939915, 448990191, 748316985, 1047643779, 1208819745, 1746072965, 2244950955, 3142931337, 5238218895, 15714656685

Offset

1,1

Comments

A subsequence of A077816.

Odd numbers n > 1 such that A237292((n-1)/2) = 1.

Indices k such that A077816(k) is not in this sequence are 2, 13, 14, 16, 22, 24, 25, 27, 28, 30, ... - Altug Alkan, Dec 11 2015

There are no other terms, unless there are other Wieferich primes (A001220) besides 1093 and 3511. - Max Alekseyev, Dec 11 2015

Links

Table of n, a(n) for n=1..43.

Mathematica

Select[Range[10^6], Mod[2^MultiplicativeOrder[2, 2 ((# - 1)/2) + 1], #^2] == 1 &] (* Michael De Vlieger, Dec 11 2015 *)

Prog

(PARI) a002326(n) = znorder(Mod(2, 2*n+1));
a237292(n) = a002326(2*n*(n+1))/a002326(n);
for(n=1, 1e8, if(a237292(n)==1, print1(2*n+1, ", "))) \\ Altug Alkan, Dec 11 2015

Crossrefs

Cf. A002326, A077816, A237292.

Sequence in context: A077816 A291961 A001220 * A355545 A291194 A331021

Adjacent sequences: A265627 A265628 A265629 * A265631 A265632 A265633

Keyword

nonn

Author

Thomas Ordowski, Dec 11 2015

Extensions

More terms from Altug Alkan, Dec 11 2015

Missing terms a(28)-a(30) and further terms a(34)-a(43) added by Max Alekseyev, Dec 11 2015

Status

approved