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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture: Sequence is infinite.
LINKS
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
Sequence in context: A300458 A041917 A318089 * A181756 A287874 A064841
KEYWORD
base,nonn
AUTHOR
Jason Earls, Jun 24 2005
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)