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%I #23 Feb 09 2021 01:55:10
%S 55,253,275,385,605,715,935,1045,1081,1265,1375,1595,1705,1711,1771,
%T 1925,2035,2255,2365,2485,2585,2695,2783,2915,3025,3245,3289,3355,
%U 3403,3575,3685,3905,4015,4235,4301,4345,4565,4675,4807,4895,5005,5225,5335,5405,5555
%N Numbers k such that k == 1 or -1 (mod 6) but k does not divide the numerator of Bernoulli(2*k).
%p isa := n -> abs(mods(n, 6)) = 1 and modp(numer(bernoulli(2*n)), n) <> 0:
%p select(isa, [$1..2255]); # _Peter Luschny_, Aug 02 2017
%t Select[Range@9999,0 != Mod[Numerator@BernoulliB[2 #], #] && MemberQ[{1, 5}, Mod[#, 6]] &]
%o (PARI) isok(n) = (((n % 6) == 1) || ((n % 6) == 5)) && (numerator(bernfrac(2*n)) % n); \\ _Michel Marcus_, Aug 02 2017
%Y Cf. A000367, A286853 (1st differences).
%K nonn
%O 1,1
%A _Bill Gosper_, Aug 01 2017