cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A216827 Numbers whose squares can be written neither as a^2 + b^2, nor as a^2 + 2*b^2, nor as a^2 + 3*b^2, nor as a^2 + 7*b^2, with a > 0 and b > 0.

This page as a plain text file.
%I A216827 #11 Sep 22 2022 01:50:14
%S A216827 1,47,167,311,383,479,503,647,719,839,887,983,1151,1223,1319,1487,
%T A216827 1511,1559,1823,1847,2063,2209,2351,2399,2663,2687,2903,2999,3023,
%U A216827 3167,3191,3359,3407,3527,3671,3863,3911,4007,4079,4583,4679,4703,4751,4871,4919,5039,5087,5351,5519,5591,5711,5879,5927
%N A216827 Numbers whose squares can be written neither as a^2 + b^2, nor as a^2 + 2*b^2, nor as a^2 + 3*b^2, nor as a^2 + 7*b^2, with a > 0 and b > 0.
%C A216827 If a composite number C can be written in the form C = a^2+k*b^2, for some integers a and b, then every prime factor P (for C) being raised to an odd power can be written in the form P = c^2+k*d^2, for some integers c and d.
%C A216827 This statement is only true for k = 1, 2, 3.
%C A216827 For k = 7, with the exception of the prime factor 2, the statement mentioned above is true.
%Y A216827 Cf. A216451, A216500, A216501, A216671, A216679, A216680, A216682.
%K A216827 nonn
%O A216827 1,2
%A A216827 _V. Raman_, Sep 17 2012