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Search: id:A122035
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| A122035 |
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Primes p = Prime[m] such that polynomial (1 + Sum[x^Prime[k],{k,1,m}]) factors over the integers. |
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1
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OFFSET
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1,1
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COMMENT
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Corresponding numbers m such that a(n) = Prime[m] are {3,7,13,89,...}. All 4 listed initial terms of a(n) coincide with A007351[n+1].
The polynomial is divisible by x^2+1 if and only if p is a member of A007351. - David Wasserman (dwasserm(AT)earthlink.net), May 20 2008
No other terms below 4175. - Max Alekseyev (maxal(AT)cs.ucsd.edu), May 31 2008
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EXAMPLE
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a(1) = 5 because Factor[1+x^2+x^3+x^5] = (x+1)*(x^2+1)*(x^2-x+1), but polynomials (1+x^2) and (1+x^2+x^3) do not factor over the integers.
a(2) = 17 because Factor[1+x^2+x^3+x^5+x^7+x^11+x^13+x^17] = (x^2+1)*(x^15-x^13+2x^11-x^9+x^7+x^3+1).
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CROSSREFS
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Cf. A038691, A007351.
Sequence in context: A111268 A106973 A102264 this_sequence A052350 A096741 A111746
Adjacent sequences: A122032 A122033 A122034 this_sequence A122036 A122037 A122038
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KEYWORD
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more,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 13 2006
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