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A135516
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a(0)=1; a(n)= [product_(i=1..n) p(i)^2] - 1, where p(i) is i-th prime.
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1
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1, 3, 35, 899, 44099, 5336099, 901800899, 260620460099, 94083986096099, 49770428644836899, 41856930490307832899, 40224510201185827416899, 55067354465423397733736099, 92568222856376731590410384099
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sequence generalized: a(0)=1; a(n)=[product_(i=1..n) p(i)^r]-1, where p(i) is i-th prime.
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REFERENCES
| A. Adelberg, S. Hong and W. Ren, Bounds on divided universal Bernoulli numbers and universal Kummer congruences, Proc. Amer. Math. Soc., Volume 136, Number 1, 2008, Pages 61-71, http://www.math.grin.edu/faculty/Adelberg-Bounds-of.pdf
Alexei A. Panchishkin; Generalized Kummer congruences and p-adic families of motives, http://arXiv.org/abs/math/9503218
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FORMULA
| a(n) = A061742(n-1)-1 = [A002110(n)+1]*[A002110(n)-1] for n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 28 2008
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MAPLE
| A002110 := proc(n) mul(ithprime(i), i=1..n) ; end: A135516 := proc(n) if n =0 then 1; else (A002110(n)+1)*(A002110(n)-1) ; fi ; end: seq(A135516(n), n=0..20) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 28 2008
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MATHEMATICA
| Join[{1}, Rest[#-1&/@FoldList[Times, 1, Prime[Range[15]]^2]]] (* From Harvey P. Dale, Oct 02 2011 *)
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CROSSREFS
| Cf. A057588, A057705, A002110.
Sequence in context: A093531 A129505 A185752 * A107712 A062699 A012767
Adjacent sequences: A135513 A135514 A135515 * A135517 A135518 A135519
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KEYWORD
| easy,nonn
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AUTHOR
| Ctibor O. ZIZKA (zizka(AT)seznam.cz), Feb 19 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 28 2008
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