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

1,1

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

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 *)

Crossrefs

Cf. A034708.

Sequence in context: A085878 A238633 A266815 * A239897 A138075 A222315

Adjacent sequences: A064776 A064777 A064778 * A064780 A064781 A064782

Keyword

base,nonn

Author

Santi Spadaro, Oct 19 2001

Status

approved