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A182404
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Numbers whose digit sum as well as sum of the squares of the digits is a prime.
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2
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11, 12, 14, 16, 21, 23, 25, 32, 38, 41, 49, 52, 56, 58, 61, 65, 83, 85, 94, 101, 102, 104, 106, 110, 111, 113, 119, 120, 131, 133, 137, 140, 146, 160, 164, 166, 173, 179, 191, 197, 199, 201, 203, 205, 210, 223, 229, 230, 232, 250, 289, 292, 298, 302, 308
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OFFSET
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1,1
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COMMENTS
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Note that the cube analog "Numbers whose digit sum as well as sum of the cubes of the digits is a prime" only occurs when A007953(n) = Digital sum (i.e., sum of digits) of n) = 2, as otherwise A055012(n) = Sum of cubes of digits of n = 2, i.e., n = 2, 11, 20, 101, 110, 1001, 1010, ... since for natural numbers A^3 + B^3 is divisible by A+B. Hence "Numbers whose digit sum as well as sum of the cubes of the digits is a prime" begins 2, 11, 101, ... . - Jonathan Vos Post, May 10 2012
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LINKS
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EXAMPLE
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25 is here because 2 + 5 = 7 and 2*2 + 5*5 = 29 both are prime.
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MATHEMATICA
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fQ[n_] := Module[{d = IntegerDigits[n]}, PrimeQ[Total[d]] && PrimeQ[Total[d^2]]]; Select[Range[500], fQ] (* T. D. Noe, May 09 2012 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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