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Search: id:A156859
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| A156859 |
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The main column of a version of the "Ulam spiral". |
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+0
2
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| 0, 3, 7, 14, 22, 33, 45, 60, 76, 95, 115, 138, 162, 189, 217, 248, 280, 315, 351, 390, 430, 473, 517, 564, 612, 663, 715, 770, 826, 885, 945, 1008, 1072, 1139, 1207
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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It is easy to see that the only two primes in the sequence are 3, 7. Therefore the primes of the version of "Ulam spiral" are divided into four parts (see also A035608): north-east (NE), north-west (NW), south-west (SW), and south-east (SE).
a(n) = [b(n) U c(n)], being b(n)=4*n^2+3*n and c(n)=4*n^2+7*n+3 with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Mar 05 2009]
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LINKS
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E. Apricena, A version of "Ulam Spiral" divided into four parts.
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FORMULA
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a(n)=n^2+n+[(n+1)/2]
G.f.: x(3+x)/((1+x)(1-x)^3). a(n)=2*a(n-1)-2*a(n-3)+a(n-4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009
a(n)=-n-1+Sum_{j=0..n}Sum_{k=0..j}[2+(-1)^k] [From Paolo P. Lava (ppl(AT)spl.at), Mar 05 2009]
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MAPLE
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P:=proc(i) local a, j, k, n; for n from 0 by 1 to i do a:=sum(sum(2-(-1)^k, k=0..j), j=0..n)-n-1; print(a); od; end: P(100); [From Paolo P. Lava (ppl(AT)spl.at), Mar 05 2009]
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CROSSREFS
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Cf. A035608.
A115258 [From Paolo P. Lava (ppl(AT)spl.at), Mar 05 2009]
Sequence in context: A033808 A161210 A154772 this_sequence A146931 A115285 A004232
Adjacent sequences: A156856 A156857 A156858 this_sequence A156860 A156861 A156862
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KEYWORD
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nonn
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AUTHOR
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Emilio Apricena (emilioapricena(AT)yahoo.it), Feb 17 2009
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