A122631 a(n+1) = gpf(2*prime(a(n-1)) + prime(a(n))) where gpf = greatest prime factor, with a(0)=1, a(1)=2.

1, 2, 7, 23, 13, 23, 11, 197, 421, 113, 13, 17, 47, 47, 211, 191, 1249, 499, 1039, 79, 97, 23, 367, 881, 337, 409, 2447, 277, 857, 487, 61, 83, 997, 53, 16007, 1033, 43, 16657, 101, 67, 19, 3, 139, 269, 107, 109, 197, 2399, 7927, 41257, 47, 103, 197, 179, 11, 719, 5503

Offset

0,2

Comments

This sequence is eventually cyclic with period 360.

Links

Reinhard Zumkeller and Charles R Greathouse IV, Table of n, a(n) for n = 0..10000 (terms below 97 from Zumkeller)

Example

2*prime(7) + prime(23) = 2*17 + 83 = 117 = 3*3*13, so a(4) = gpf(117) = 13.

Mathematica

Transpose[NestList[{#[[2]], FactorInteger[2Prime[ #[[1]]] +Prime[ #[[2]]]][[ -1, 1]]} &, {1, 2}, 900]][[2]]

Prog

(Haskell)
a122631 n = a122631_list !! (n-1)
a122631_list =
   1 : 2 : map a006530 (zipWith (+) (map ((2 *) . a000040) a122631_list)
                                    (map a000040 (tail a122631_list)))
-- Reinhard Zumkeller, Aug 07 2011
(PARI) a=[1, 2]; for(n=2, 50, my(f=factor(2*prime(a[n-1])+prime(a[n]))[, 1]); a=concat(a, f[#f])); a \\ Charles R Greathouse IV, Jun 19 2013

Crossrefs

Cf. A006530.

Sequence in context: A153551 A125285 A170870 * A269313 A147969 A235985

Adjacent sequences: A122628 A122629 A122630 * A122632 A122633 A122634

Keyword

nice,nonn,easy

Author

Carlos Alves, Oct 29 2006

Extensions

Offset fixed and initial 1 prepended by Reinhard Zumkeller, Aug 07 2011

Status

approved