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Search: id:A002471
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| A002471 |
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Number of partitions of n into a prime and a square.
(Formerly M0073 N0025)
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+0
6
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| 0, 1, 2, 1, 1, 2, 2, 1, 1, 0, 3, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 3, 1, 0, 1, 3, 2, 2, 2, 1, 3, 2, 0, 2, 1, 1, 4, 2, 1, 3, 2, 2, 2, 2, 1, 4, 2, 1, 1, 2, 2, 3, 3, 1, 3, 2, 0, 3, 2, 1, 4, 2, 0, 2, 3, 3, 4, 2, 1, 3, 3, 2, 1, 3, 1, 4, 2, 2, 3, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(A014090(n))=0; a(A014089(n))>0; a(A143989(n))=1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 07 2008]
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REFERENCES
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Selmer, Ernst S.; Eine numerische Untersuchung ueber die Darstellung der natuerlichen Zahlen als Summe einer Primzahl und einer Quadratzahl. Arch. Math. Naturvid. 47, (1943). no. 2, 21-39.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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MAPLE
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n->nops(select(isprime, [ seq(n-i^2, i=0..trunc(sqrt(n))) ])):
with(combstruct): specM0073 := {N=Prod(P, S), P=Set(Z, card>=1), S=Set(Z, card>=0)}: `combstruct/compile`(specM0073, unlabeled): `combstruct/Count`[ specM0073, unlabeled ][ P ] := proc(p) option remember; if isprime(p) then 1 else 0 fi end: `combstruct/Count`[ specM0073, unlabeled ][ S ] := proc(p) option remember; if type(sqrt(p), integer) then 1 else 0 fi end: M0073 := n->count([ N, specM0073, unlabeled ], size=n):
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CROSSREFS
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A064272. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 07 2008]
Sequence in context: A034798 A115236 A064286 this_sequence A091243 A037826 A079882
Adjacent sequences: A002468 A002469 A002470 this_sequence A002472 A002473 A002474
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Sequence corrected by Paul Zimmermann Mar 15 1996
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