

A190680


Primes p such that sopfr(p1) = sopfr(p+1) is also prime, where sopfr is A001414.


4



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
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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 A012154
Adjacent sequences: A190677 A190678 A190679 * A190681 A190682 A190683


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV, May 16 2011


STATUS

approved



