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A136117 Pentagonal numbers (A000326) which are the sum of 2 other positive pentagonal numbers. 6
70, 92, 852, 925, 1247, 1426, 1926, 2625, 3577, 5192, 6305, 6501, 7107, 7740, 7957, 8177, 8626, 9560, 10292, 12927, 13207, 14652, 15555, 16172, 18095, 20475, 20827, 21901, 22265, 22632, 23002, 23751, 24130, 28497, 29330, 31032, 33227, 33675 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that every integer and hence every pentagonal number, greater than 33066, hence greater than A000326(149) = 33227, can be represented as the sum of three pentagonal numbers. - Jonathan Vos Post, Dec 18 2007

LINKS

Table of n, a(n) for n=1..38.

FORMULA

a(n)=A000326(A136116(n))=A000326(m)+A136114(m) where m is the index of the n-th nonzero term in A136114 or A136115.

EXAMPLE

a(1)=70=P(7) is the least pentagonal number which can be written as sum of two other pentagonal numbers, P(7)=P(5)+P(5).

PROG

(PARI) P(n)=n*(3*n-1)>>1 /* a.k.a. A000326 */

isPent(t)=P(sqrtint(t<<1\3)+1)==t

for(i=1, 299, for(j=1, (i+1)\sqrt(2), isPent(P(i)-P(j))&print1(P(i)", ")|next(2)))

/* The following is much faster, at the cost of implementing sum2sqr(), cf. A133388*/

A136117next(i)={i=sqrtint(i\3*2)*6+5; until(0, for(j=2, #t=sum2sqr((i+=6)^2+1), t[j]%6==[5, 5]&break(2))); i^2\24}

A136117vect(n, i)=vector(n, j, i=A136117next(i)) /* 2nd arg =0 by default but allows one to start elsewhere */

A136117(n, i)={until(!n--, i=A136117next(i)); i} \\ - M. F. Hasler, Dec 25 2007

CROSSREFS

Cf. A000326, A136112-A136118, A007527.

Sequence in context: A114838 A036191 A165632 * A224553 A156718 A007621

Adjacent sequences:  A136114 A136115 A136116 * A136118 A136119 A136120

KEYWORD

nonn

AUTHOR

M. F. Hasler, Dec 15 2007; corrected Dec 25 2007

STATUS

approved

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.