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Search: id:A136116
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| A136116 |
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Indices of pentagonal numbers (A000326) which are the sum of 2 other positive pentagonal numbers. |
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+0
2
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| 7, 8, 24, 25, 29, 31, 36, 42, 49, 59, 65, 66, 69, 72, 73, 74, 76, 80, 83, 93, 94, 99, 102, 104, 110, 117, 118, 121, 122, 123, 124, 126, 127, 138, 140, 144, 149, 150, 152, 161, 163, 168, 169, 174, 175, 178, 181, 185, 188, 190, 195, 199, 203, 209, 210, 212, 213
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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A000326(a(n))=A000326(m)+A136114(m) where m is the index of the n-th nonzero term in A136114 or A136115.
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EXAMPLE
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a(1)=7 since P(7)=70 is the least pentagonal number which can be written as sum of two other pentagonal numbers, P(7)=P(5)+P(5).
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PROGRAM
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(PARI) P(n)=n*(3*n-1)>>1 /* a.k.a. A000326 */
isPent(t)=P(sqrtint(t<<1\3)+1)==t
for(i=1, 999, for(j=1, (i+1)\sqrt(2), isPent(P(i)-P(j))&print1(i", ")|next(2)))
/* The following are much faster, at the cost of implementing sum2sqr(), cf. A133388. */
A136116next(i)={i=6*i-1; until(0, for(j=2, #t=sum2sqr((i+=6)^2+1), t[j]%6==[5, 5]&break(2))); i\6+1}
A136116vect(n, i=0)=vector(n, j, i=A136116next(i))
A136116(n, i=0)={until(!n--, i=A136116next(i)); i} \\ - M. F. Hasler, Dec 25 2007
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CROSSREFS
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Cf. A000326, A136112-A136118.
Adjacent sequences: A136113 A136114 A136115 this_sequence A136117 A136118 A136119
Sequence in context: A042391 A042023 A041102 this_sequence A080982 A042875 A048064
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 15 2007; corrected Dec 25 2007
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