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A118235 Smallest positive number starting an interval of consecutive integers with element sum n. 11
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

COMMENTS

Right border of A299765. - Omar E. Pol, Jul 24 2018

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Paul D. Hanna)

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. - 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.

MAPLE

a:= proc(n) local j, k, s; j, k, s:= 1$3;

      do if s=n then break fi;

         if s<n then k:= k+1; s:= s+k

                else s:= s-j; j:= j+1 fi

      od: j

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Aug 05 2018

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, Oct 28 2011 */

CROSSREFS

Cf. A000079, A000217, A001227, A002817, A104512, A109814, A212652, A299765.

Sequence in context: A243070 A243060 A286321 * A304624 A083653 A278290

Adjacent sequences:  A118232 A118233 A118234 * A118236 A118237 A118238

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 18 2006

STATUS

approved

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Last modified January 23 06:15 EST 2019. Contains 319374 sequences. (Running on oeis4.)