The On-Line Encyclopedia of Integer Sequences (OEIS)

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A136115

Index m of least pentagonal number P(m) > P(n) such that P(m)+P(n) is again a pentagonal number, 0 if no such m exists.
(history; published version)

#2 by Russ Cox at Sat Mar 31 13:48:25 EDT 2012

AUTHOR

_M. F. Hasler (Maximilian.Hasler(AT)gmail.com), _, Dec 15 2007

Discussion

Sat Mar 31

13:48

OEIS Server: https://oeis.org/edit/global/893

#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

NAME

Index m of least pentagonal number P(m) > P(n) such that P(m)+P(n) is again a pentagonal number, 0 if no such m exists.

DATA

0, 0, 0, 7, 0, 0, 23, 0, 0, 48, 0, 22, 82, 47, 0, 125, 26, 0, 22, 37, 71, 238, 0, 0, 26, 166, 0, 52, 207, 147, 117, 99, 87, 572, 72, 67, 63, 357, 57, 110, 416, 51, 917, 82, 47, 1050, 217, 380, 167, 246, 0, 97, 697, 0, 374, 191, 537, 1672, 152, 112, 136, 380, 215, 2037, 68

OFFSET

1,4

FORMULA

a(n)=0 iff n is in A136112 iff A000326(n) is in A136113.

EXAMPLE

a(1..3)=0 since P(1),P(2),P(3) cannot be written as difference of 2 other pentagonal numbers > 0.

a(4)=7 since P(7)=70 is the least pentagonal number > P(4)=22 such that their sum is again a pentagonal number, P(8).

PROG

(PARI) P(n)=n*(3*n-1)>>1 /* a.k.a. A000326 */ /* newline */ isPent(t)=P(sqrtint(t<<1\3)+1)==t /* newline */ for(i=1, 99, for(j=i+1, (P(i)-1)\3, isPent(P(i)+P(j))&print1(j", ")|next(2)); print1(0", "))

CROSSREFS

Cf. A000326, A136112-A136118.

KEYWORD

nonn

AUTHOR

M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 15 2007

STATUS

approved