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A118235 Smallest number summing up to n together with some succeeding consecutive numbers. 10
1, 2, 1, 4, 2, 1, 3, 8, 2, 1, 5, 3, 6, 2, 1, 16, 8, 3, 9, 2, 1, 4, 11, 7, 3, 5, 2, 1, 14, 4, 15, 32, 3, 7, 2, 1, 18, 8, 4, 6, 20, 3, 21, 2, 1, 10, 23, 15, 4, 8, 6, 3, 26, 2, 1, 5, 7, 13, 29, 4, 30, 14, 3, 64, 2, 1, 33, 5, 9, 7, 35, 4, 36, 17, 3, 6, 2, 1, 39, 14, 5, 19, 41, 7, 4, 20, 12, 3, 44, 2, 1, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..1000

FORMULA

A109814(n) * (A109814(n) + 2*a(n) - 1) / 2 = n.

a(m) = n iff m = 2^k: a(A000079(n)) = A000079(n);

a(m) = 1 iff m = k*(k+1)/2: a(A000217(n)) = 1.

a(A002817(n-1)+1) = n; i.e., a(m) = n if m = k*(k-1)/2 + 1 and k = n*(n-1)/2 + 1. [From Paul D. Hanna, Oct 28 2011]

EXAMPLE

a(3)=1 since 3=1+2; a(5)=2 since 5=2+3; a(6)=1 since 6=1+2+3; etc.

PROG

(PARI) {a(n)=local(A=n); for(j=1, n, for(k=j, n+1, if(n==k*(k-1)/2-j*(j-1)/2, A=j; k=j=2*n+1))); A} /* Paul D. Hanna */

CROSSREFS

Cf. A001227. A104512.

Sequence in context: A243070 A243060 A286321 * A083653 A278290 A135152

Adjacent sequences:  A118232 A118233 A118234 * A118236 A118237 A118238

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 18 2006

STATUS

approved

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Last modified February 19 16:28 EST 2018. Contains 299356 sequences. (Running on oeis4.)