A109280 Numbers n such that z(n) and z(n+1) are both prime, where z(n) = a^d + b^d + c^d + ..., where a*b*c* ... is the prime factorization of n and d is the largest digit of n.

10, 11, 567, 1209, 2034, 3114, 3311, 5243, 5290, 7256, 7436, 9558, 10110, 10111, 13251, 14409, 17536, 20344, 21534, 26411, 26816, 29078, 30232, 34160, 37074, 40022, 44849, 45373, 45815, 50630, 53577, 55555, 56030, 62355, 62463, 65540

Offset

1,1

Comments

Conjecture: Sequence is infinite.

Links

Table of n, a(n) for n=1..36.

Example

567 is in the sequence because 567 = 3^4*7 and 3^7+3^7+3^7+3^7+7^7 = 832291,
a prime; and 568 = 2^3*71 and 2^8+2^8+2^8+71^8 = 645753531246529, a prime.

Mathematica

bpQ[n_]:=Module[{pfn=Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[n]], ldn=Max[ IntegerDigits[n]], pfn1=Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[n+1]], ldn1 =Max[IntegerDigits[n+1]]}, And@@PrimeQ[{Total[ pfn^ldn], Total[pfn1^ldn1]}]]; Select[Range[70000], bpQ] (* Harvey P. Dale, Nov 14 2012 *)

Crossrefs

Cf. A082813, A109279.

Sequence in context: A300458 A041917 A318089 * A181756 A287874 A064841

Adjacent sequences: A109277 A109278 A109279 * A109281 A109282 A109283

Keyword

base,nonn

Author

Jason Earls, Jun 24 2005

Status

approved