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A053615
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Pyramidal sequence: distance to nearest product of two consecutive integers (pronic or heteromecic numbers).
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4
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0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(A002378(n))=0; a(n^2)=n.
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FORMULA
| a(n)=A004738(n+1)-1
Let u(1)=1, u(n)=n-u(n-sqrtint(n)) (cf. A037458); then a(0)=0 and for n>0 a(n)=2*u(n)-n. - Benoit Cloitre, Dec 22 2002
a(0)=0 then a(n)=floor(sqrt(n))-a(n-floor(sqrt(n))) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 03 2004
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EXAMPLE
| a(10)=|10-3*4|=2
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MATHEMATICA
| a[0] = 0; a[n_] := Floor[Sqrt[n]] - a[n - Floor[Sqrt[n]]]; Table[a[n], {n, 0, 103}] (* From Jean-François Alcover, Dec 16 2011, after Benoit Cloitre *)
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PROG
| (PARI) a(n)=if(n<1, 0, sqrtint(n)-a(n-sqrtint(n)))
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CROSSREFS
| Cf. A002262, A002378, A004738, A053188.
Sequence in context: A116433 A106509 A196199 * A002819 A037834 A179765
Adjacent sequences: A053612 A053613 A053614 * A053616 A053617 A053618
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 20 2000
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