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A279065 Fermi-Dirac primeth recurrence: a(0)=1; thereafter a(n+1) = a(n)-th number of the form p^(2^k) where p is prime and k>=0. 16
1, 2, 3, 4, 5, 7, 11, 19, 47, 169, 907, 6829, 67931, 851891, 13034887 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Forgues (see A182979) and Zumkeller (see A213925) describe the increasing sequence of positive integers of the form p^(2^k) where p is prime and k>=0 (A050376 or A084400) as Fermi-Dirac primes, because any positive integer has a unique factorization into distinct terms.

LINKS

Table of n, a(n) for n=0..14.

OEIS Wiki, "Fermi-Dirac representation" of n

MATHEMATICA

nn=10000; FDfactor[n_]:=If[n===1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];

FDprimeList=Array[FDfactor, nn, 1, Union];

NestWhileList[Part[FDprimeList, #]&, 1, #<=Length[FDprimeList]&]

CROSSREFS

Cf. A007097, A050376, A084400, A182979, A213925.

Sequence in context: A018134 A245823 A143284 * A327325 A324989 A015856

Adjacent sequences:  A279062 A279063 A279064 * A279066 A279067 A279068

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 10 2016

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)