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A079062 a(1) = 2; for n>1, a(n) = smallest prime p such that p - a(n-1) = a^b for some positive integers a,b > 1. 2
2, 11, 19, 23, 31, 47, 79, 83, 211, 227, 263, 271, 307, 311, 347, 379, 383, 419, 547, 563, 571, 587, 619, 683, 691, 727, 743, 751, 787, 823, 827, 859, 863, 991, 1091 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

EXAMPLE

Start with 2. 2 + 3^2 = 11 is a prime and there is no smaller such prime, so 11 is the next number. 11 + 2^3 = 19 is a prime and there is no smaller such prime, so 19 comes next, etc.

MATHEMATICA

a[1] = 2; a[n_] := a[n] = Catch[ For[p = NextPrime[a[n-1]], True, p = NextPrime[p], q = p - a[n-1]; test = Catch[ Do[ If[q == a^b, Throw[True]], {a, 2, Ceiling[Sqrt[q]]}, {b, 2, Ceiling[Log[2, q]]}]]; If[test === True, Throw[p]]]]; Table[a[n], {n, 1, 35}] (* Jean-Fran├žois Alcover, Jul 13 2012 *)

PROG

(Haskell)

a079062 n = a079062_list !! (n-1)

a079062_list = 2 : f 2 (tail a000040_list) where

   f x ps = q : f q qs where

     (q:qs) = dropWhile (\p -> a075802 (p - x) == 0 || p - x == 1) ps

-- Reinhard Zumkeller, Jun 14 2013

CROSSREFS

Cf. A075802, A000040.

Sequence in context: A023173 A018443 A163058 * A038930 A019375 A078784

Adjacent sequences:  A079059 A079060 A079061 * A079063 A079064 A079065

KEYWORD

nice,nonn

AUTHOR

Fabian Rothelius, Feb 02 2003

STATUS

approved

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Last modified December 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)