A064779 Primes such that the sum of their digits and the sum of the reciprocals of their digits is also prime.

11, 2441, 4241, 4421, 12163, 12613, 13313, 13331, 16231, 16363, 16633, 21163, 21613, 26113, 31663, 32233, 32323, 32611, 33113, 33223, 33311, 48281, 48821, 61231, 61363, 62131, 62311, 63211, 63361, 88241

Offset: 1

Author

Santi Spadaro, Oct 19 2001

Keywords

• base
• nonn

Comments

Zero, five, and seven never appear as a digit of any of the terms of this sequence. - Harvey P. Dale, Jul 17 2013

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034708.

Programs

Mathematica

f[ n_ ] := 1/n a[ n_ ] := Apply[ Plus, Map[ f, IntegerDigits[ n ] ] ] b[ n_ ] := Apply[ Plus, IntegerDigits[ n ] ] Select[ Range[ 100000 ], FreeQ[ IntegerDigits[ # ], 0 ] && PrimeQ[ a[ # ] ] && PrimeQ[ b[ # ] ] && PrimeQ[ # ] & ]
sdpQ[n_]:=Module[{idn=IntegerDigits[n]},Min[idn]>0&&And@@PrimeQ[{Total[ idn], Total[ 1/idn]}]]; Select[Prime[Range[10000]],sdpQ] (* Harvey P. Dale, Jul 17 2013 *)