A006971 Composite numbers k such that k == +-1 (mod 8) and 2^((k-1)/2) == 1 (mod k). (Formerly M5461)

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

1,1

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)

Mathematica

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

Crossrefs

Subsequence of A001567 and A047713.

Cf. A244626, A244628, A270697, A270698.

Sequence in context: A290486 A253595 A047713 * A270698 A218483 A309235

Adjacent sequences: A006968 A006969 A006970 * A006972 A006973 A006974

Keyword

nonn

Author

Richard Pinch

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

Status

approved