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

Author

Michel Lagneau, Dec 21 2010

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

Cf. A139749 A139750

Programs

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]