A006971 Composite numbers k such that k == +-1 (mod 8) and 2^((k-1)/2) == 1 (mod k).

561, 1105, 1729, 1905, 2047, 2465, 4033, 4681, 6601, 8321, 8481, 10585, 12801, 15841, 16705, 18705, 25761, 30121, 33153, 34945, 41041, 42799, 46657, 52633, 62745, 65281, 74665, 75361, 85489, 87249, 90751, 113201, 115921, 126217, 129921, 130561, 149281, 158369

Offset: 1

Author

Richard Pinch

Keywords

• nonn

Comments

Previous name was "Terms of A047713 that are congruent to +-1 mod 8".

Complement of (A244626 union A244628) with respect to A047713. - Jianing Song, Sep 18 2018

References

• Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A12, pp. 44-50.
• Hans Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..828 from Jianing Song using data from A047713)

Crossrefs

Subsequence of A001567 and A047713.

Cf. A244626, A244628, A270697, A270698.

Programs

Mathematica

Select[Range[10^5], MemberQ[{1, 7}, Mod[#, 8]] && CompositeQ[#] && PowerMod[2, (# - 1)/2, #] == 1 &] (* Amiram Eldar, Nov 06 2023 *)

Extensions

This sequence appeared as M5461 in Sloane-Plouffe (1995), but was later mistakenly declared to be an erroneous form of A047713. Thanks to Jianing Song for providing the correct definition. - N. J. A. Sloane, Sep 17 2018

Formal definition by Jianing Song, Sep 18 2018