Cheers,

EDITS OF A112054, A112055 (both submitted yesterday) and A047621.

It's also easy to see, that A112054 are indeed always divisible
by 6, so this necessitates a change of the conjectural tone
in a couple of sequences I recently submitted:

%I A112054
%S A112054 12,18,30,42,48,72,78,90,102,108,120,132,138,162,168,180,192,198,210,
%T A112054 222,228,240,252,258,282,288,300,312,318,330,342,348,372,378,390,402,
%U A112054 408,420,432,438,450,462,468,492,498,510,522,528,540,552,558,582,588
%N A112054 Points where A112053 is not zero.
%C A112054 These are all divisible by six, as J(2,m) = +1 if m = 1 or 7 mod 8, and -1 if m = 3 or 5 mod 8 and J(3,m) = +1 if m = 1 or 11 mod 12, -1 if m = 5 or 7 mod 12, and 0 if m = 3 or 9 mod 12 (where Jacobi symbol J(i,m) returns +1 if i is quadratic residue modulo odd number m), it follows that only when i=24*n it holds that J(2,i-1)=J(2,i+1)=J(3,i-1)=J(3,i+1)=+1, and thus only then the function A112046 (and A112053) depends on values of J(k>3,m).
%Y A112054 A112058(n) = 4*a(n). A112055(n) = a(n)/6.
%K A112054 nonn
%O A112054 1,1
%A A112054 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Aug 27 2005


%I A112055
%S A112055 2,3,5,7,8,12,13,15,17,18,20,22,23,27,28,30,32,33,35,37,38,40,42,43,
%T A112055 47,48,50,52,53,55,57,58,62,63,65,67,68,70,72,73,75,77,78,82,83,85,87,
%U A112055 88,90,92,93,97,98,100,102,103,107,108,110,112,113,117,118,120,122
%N A112055 A112054(n)/6.
%Y A112055 Complement: A112082. First differences: A112085.
%K A112055 nonn
%O A112055 1,1
%A A112055 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Aug 27 2005


%I A047621
%S A047621 3,5,11,13,19,21,27,29,35,37,43,45,51,53,59,61,67,69,75,77,83,85,91,93,
%T A047621 99,101,107,109,115,117,123,125,131,133,139,141,147,149,155,157,163,
%U A047621 165,171,173,179,181,187,189
%N A047621 Numbers that are congruent to {3, 5} mod 8.
%C A047621 Odd numbers n such that x^2 == 2 (mod n) has no solution, i.e. those n for which Jacobi symbol J(2,n) = -1.
%Y A047621 Adjacent sequences: A047618 A047619 A047620 this_sequence A047622 A047623 A047624
%Y A047621 Sequence in context: A062391 A038951 A020578 this_sequence A066587 A045405 A059311
%Y A047621 Row 1 of A112070. Complement of A047522 relative to A005408. Primes in this sequence: A003629.
%K A047621 nonn
%O A047621 0,1
%A A047621 njas