A094551 - OEIS

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

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OFFSET

1,1

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)

LINKS

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

EXAMPLE

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

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<s2, i1--; s1=s1+i1, i2++; s2=s2+i2]]; If[s1==s2, AppendTo[lst, n]], {n, 2, 140}]; lst

CROSSREFS

Cf. A002144, A094550, A094552, A094553.

Sequence in context: A112680 A096079 A298984 * A342006 A239937 A375019

Adjacent sequences: A094548 A094549 A094550 * A094552 A094553 A094554

KEYWORD

nonn

AUTHOR

T. D. Noe, May 10 2004

STATUS

approved