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A109280
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Conjecture: Sequence is infinite.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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