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A072502 Numbers that are run sums (trapezoidal, the difference between two triangular numbers) in exactly 3 ways. 11
9, 18, 25, 36, 49, 50, 72, 98, 100, 121, 144, 169, 196, 200, 242, 288, 289, 338, 361, 392, 400, 484, 529, 576, 578, 676, 722, 784, 800, 841, 961, 968, 1058, 1152, 1156, 1352, 1369, 1444, 1568, 1600, 1681, 1682, 1849, 1922, 1936, 2116, 2209, 2304, 2312, 2704 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also numbers that are the product of a binary power (cf. A000079) and a square of an odd prime, or numbers having exactly 3 odd divisors: A001227(a(n)) = 3. - Reinhard Zumkeller, May 01 2012

Numbers n such that the symmetric representation of sigma(n) has 3 subparts. - Omar E. Pol, Dec 28 2016

Also numbers that can be expressed as the sum of k > 1 consecutive positive integers in exactly 2 ways. E.g., 2+3+4 = 9 and 4+5 = 9, 3+4+5+6 = 18 and 5+6+7 = 18. - Julie Jones, Aug 13 2018

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Ron Knott, Runsums

T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.

EXAMPLE

a(1)=9 is the smallest number with 3 run sums: 2+3+4 = 4+5 = 9.

PROG

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a072502 n = a072502_list !! (n-1)

a072502_list = f (singleton 9) $ drop 2 a001248_list where

   f s (x:xs) = m : f (insert (2 * m) $ insert x s') xs where

                (m, s') = deleteFindMin s

-- Reinhard Zumkeller, May 01 2012

CROSSREFS

Not to be confused with A069562.

Cf. A001227, A001248, A038547, A038550, A237593, A279387.

Sequence in context: A038837 A034046 A069562 * A195268 A227279 A102042

Adjacent sequences:  A072499 A072500 A072501 * A072503 A072504 A072505

KEYWORD

easy,nonn

AUTHOR

Ron Knott, Jan 27 2003

EXTENSIONS

Extended by Ray Chandler, Dec 30 2011

STATUS

approved

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Last modified October 15 22:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)