A190680 Primes p such that sopfr(p-1) = sopfr(p+1) is also prime, where sopfr is A001414.

11, 251, 1429, 906949, 1050449, 1058389, 3728113, 9665329, 13623667, 14320489, 30668003, 30910391, 45717377, 49437001, 55544959, 57510911, 58206653, 58772257, 69490901, 72191321, 73625789, 75235973, 79396433, 99673891, 103821169, 104662139, 121322449, 125938889, 147210257, 164810311, 169844879, 170650169, 201991721

Offset

1,1

Comments

The first three terms were computed by J. M. Bergot (personal communication from J. M. Bergot to N. J. A. Sloane, May 16 2011).

The number of terms < 10^n: 0, 1, 2, 3, 3, 4, 8, 24, 70, 253, 839, ..., . - Robert G. Wilson v, May 31 2011

Links

Charles R Greathouse IV and Robert G. Wilson v, Table of n, a(n) for n = 1.. 2592 (Charles R Greathouse IV to 1536, Robert G. Wilson v to 2592)

Example

sopfr(250) = sopfr(2*5^3) = 2 + 5*3 = 17 = 2*2 + 3*2 + 7 = sopfr(2^2*3^2*7) = sopfr(252), and 17 and 251 are prime, so 251 is in this sequence.

Mathematica

f[n_] := Plus @@ Flatten[ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]; fQ[n_] := Block[{pn = f[n - 1], pp = f[n + 1]}, pn == pp && PrimeQ@ pn]; p = 2; lst = {}; While[p < 216000000, If[ fQ@ p, AppendTo[lst, p]]; p = NextPrime@ p]; lst (* Robert G. Wilson v, May 18 2011 *)

Crossrefs

Subsequence of A086711. Cf. A190722.

Sequence in context: A098672 A056210 A182350 * A089298 A274129 A346896

Adjacent sequences: A190677 A190678 A190679 * A190681 A190682 A190683

Keyword

nonn

Author

Charles R Greathouse IV, May 16 2011

Status

approved