A081467 a(n) = smallest (n+k) such that n divides the sum (n+1)+ (n+2) + ... (n+k) = k*n + k*(k+1)/2.

2, 5, 5, 11, 9, 9, 13, 23, 17, 14, 21, 20, 25, 21, 20, 47, 33, 26, 37, 35, 27, 33, 45, 39, 49, 38, 53, 35, 57, 45, 61, 95, 44, 50, 49, 44, 73, 57, 51, 55, 81, 62, 85, 76, 54, 69, 93, 80, 97, 74, 68, 91, 105, 81, 65, 104, 75, 86, 117, 75, 121, 93, 90, 191, 90, 77, 133, 84, 92, 90, 141, 135, 145

Offset

1,1

Comments

The condition can obviously be simplified to "n divides k*(k+1)/2" (cf. A011772), which is the case when k+1 = n is odd (so k/2 is integer) or else k = n is odd, whence a(n) <= 2*n - n%2, where % is the mod/remainder operator. - M. F. Hasler, Apr 17 2025

Links

Table of n, a(n) for n=1..73.

Formula

a(n) = n + A011772(n). - M. F. Hasler, Apr 17 2025

Example

a(4) = 11 as 4 divides 5+6+7+8+9+10+11 and not a smaller sum.

Prog

(PARI) A081467(n)=A011772(n)+n \\ There are efficient programs for A011772.
apply( {A081467(n)=for(k=1, oo, k*(k+1)/2%n||return(n+k))}, [1..99]) \\ Brute-force computation, for illustration. - M. F. Hasler, Apr 17 2025

Crossrefs

Cf. A081468, A081469, A081470, A081471, A081472, A000217.

Sequence in context: A132295 A086651 A074495 * A194119 A084721 A273041

Adjacent sequences: A081464 A081465 A081466 * A081468 A081469 A081470

Keyword

nonn

Author

Amarnath Murthy, Mar 23 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

More terms from M. F. Hasler, Apr 17 2025

Status

approved