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, 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, 1123, 1187, 1223, 1231, 1427, 1459, 1523, 1531, 1567, 1571, 1579, 1583, 1619, 1627, 1663, 1667

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-François 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: A018443 A163058 A161504 * A038930 A019375 A078784

Adjacent sequences: A079059 A079060 A079061 * A079063 A079064 A079065

Keyword

nice,nonn

Author

Fabian Rothelius, Feb 02 2003

Status

approved