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A094551 Numbers k such that there are integers a < b with a+(a+1)+...+(k-1) = k+(k+1)+...+b.

%I A094551 #8 Oct 28 2024 05:13:11
%S A094551 3,7,8,9,13,15,18,19,20,21,23,26,27,28,31,33,37,38,43,44,45,46,48,49,
%T A094551 51,53,55,56,57,58,59,60,62,63,68,69,72,73,75,77,78,79,80,83,85,87,88,
%U A094551 91,92,93,94,97,98,99,102,103,108,110,111,113,115,117,118,121,123,124,128
%N A094551 Numbers k such that there are integers a < b with a+(a+1)+...+(k-1) = k+(k+1)+...+b.
%C A094551 From _Robert Israel_, Oct 28 2024: (Start)
%C A094551 Numbers k such that 2 * (2*k-1)^2 is the sum of two distinct squares.
%C A094551 Numbers k such that 2*k-1 has at least one prime factor in A002144. (End)
%H A094551 Robert Israel, <a href="/A094551/b094551.txt">Table of n, a(n) for n = 1..10000</a>
%e A094551 7 is in this sequence because 4+5+6 = 7+8.
%p A094551 filter:= proc(k)
%p A094551 member(1, numtheory:-factorset(2*k-1) mod 4)
%p A094551 end proc:
%p A094551 select(filter, [$1..1000]); # _Robert Israel_, Oct 28 2024
%t A094551 lst={}; Do[i1=n-1; i2=n; s1=i1; s2=i2; While[i1>1 && s1!=s2, If[s1<s2, i1--; s1=s1+i1, i2++; s2=s2+i2]]; If[s1==s2, AppendTo[lst, n]], {n, 2, 140}]; lst
%Y A094551 Cf. A002144, A094550, A094552, A094553.
%K A094551 nonn
%O A094551 1,1
%A A094551 _T. D. Noe_, May 10 2004