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

3, 7, 8, 9, 13, 15, 18, 19, 20, 21, 23, 26, 27, 28, 31, 33, 37, 38, 43, 44, 45, 46, 48, 49, 51, 53, 55, 56, 57, 58, 59, 60, 62, 63, 68, 69, 72, 73, 75, 77, 78, 79, 80, 83, 85, 87, 88, 91, 92, 93, 94, 97, 98, 99, 102, 103, 108, 110, 111, 113, 115, 117, 118, 121, 123, 124, 128

Offset: 1

Author

T. D. Noe, May 10 2004

Keywords

• nonn

Comments

From Robert Israel, Oct 28 2024: (Start)

Numbers k such that 2 * (2*k-1)^2 is the sum of two distinct squares.

Numbers k such that 2*k-1 has at least one prime factor in A002144. (End)

Examples

			7 is in this sequence because 4+5+6 = 7+8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A094550, A094552, A094553.

Programs

Maple

filter:= proc(k)
member(1, numtheory:-factorset(2*k-1) mod 4)
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 28 2024

Mathematica

lst={}; Do[i1=n-1; i2=n; s1=i1; s2=i2; While[i1>1 && s1!=s2, If[s1