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Search: id:A104313
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| A104313 |
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Numbers n such that the coefficient of x^(2n) in (x^4+x^3+x^2+x+1)^n is prime. |
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2
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OFFSET
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1,1
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COMMENT
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n such that A005191(n) is prime. No other n<10000. The primes are in A104314. Only coefficients of the x, x^(2n) and x^(4n-1) terms can be prime; the coefficients of x and x^(4n-1) terms are prime whenever n is prime.
No other n<195316. Most likely this sequence is finite. Terms A005191(n) that are not a multiple of 5 have zero density, namely, there are fewer than n^(log(4)/log(5)) such terms among A005191(1..n). In particular, A005191(5k+2) and A005191(5k+4) are multiples of 5 for every k. - Max Alekseyev (maxale(AT)gmail.com), Apr 25 2005
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MATHEMATICA
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f=1; Do[f=Expand[f*(x^4+x^3+x^2+x+1)]; s=Coefficient[f, x, 2n]; If[PrimeQ[s], Print[{n, s}]], {n, 100}]
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CROSSREFS
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Cf. A005191 (pentanomial coefficients).
Adjacent sequences: A104310 A104311 A104312 this_sequence A104314 A104315 A104316
Sequence in context: A010344 A037316 A032813 this_sequence A037423 A009249 A012697
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KEYWORD
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more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 01 2005
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