A178357 Numbers n such that d(1)^1 + d(2)^2 +...+ d(p)^p and d(1)^p + d(2)^p-1 +...+ d(p)^1 are prime numbers, where d(i), i=1..p, are the digits of n.

2, 3, 5, 7, 11, 12, 14, 16, 21, 23, 29, 32, 34, 38, 41, 43, 47, 56, 61, 65, 74, 83, 89, 92, 98, 101, 110, 111, 113, 115, 120, 122, 131, 133, 137, 139, 140, 146, 153, 155, 160, 164, 182, 186, 188, 191, 203, 205, 212, 214, 221, 225, 227, 230, 232, 236, 272, 281, 287, 290, 302, 304, 311, 313, 319, 320, 326, 331

Offset

1,1

Links

Table of n, a(n) for n=1..68.

Example

1583 is in the sequence because :
1 + 5^2 + 8^3 + 3^4 = 619 and 1^4 + 5^3 + 8^2 + 3^1 = 193 are prime numbers.

Maple

with(numtheory):for n from 1 to 1000 do:l:=length(n):n0:=n:s1:=0:s2:=0:for
  m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s1:=s1+u^(l-m+1):s2:=s2+u^m:od:
  if type(s1, prime)=true and type(s2, prime)=true then printf(`%d, `, n):else fi:od:

Mathematica

okQ[n_] := Module[{d=IntegerDigits[n], r}, r=Length[d]; PrimeQ[Total[d^Range[r]]] && PrimeQ[Total[d^Range[r, 1, -1]]]]; Select[Range[1000], okQ]

Crossrefs

Cf. A139749 A139750

Sequence in context: A139750 A330125 A139749 * A205667 A241506 A361851

Adjacent sequences: A178354 A178355 A178356 * A178358 A178359 A178360

Keyword

nonn,base

Author

Michel Lagneau, Dec 21 2010

Status

approved