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A359610
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Numbers k such that the sum of the 5th powers of the digits of k is prime.
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0
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11, 101, 110, 111, 119, 128, 133, 182, 188, 191, 218, 223, 227, 229, 232, 247, 272, 274, 281, 292, 313, 322, 331, 337, 346, 359, 364, 368, 373, 377, 379, 386, 395, 397, 427, 436, 463, 472, 478, 487, 539, 557, 568, 575, 577, 586, 593, 634, 638, 643, 658, 667
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OFFSET
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1,1
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COMMENTS
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It is easy to establish that the sequence is infinite: if x is in the sequence, so is 10*x.
Alternatively: the sequence is infinite as the sequence contains all numbers consisting of a prime number of 1s and an arbitrary number of 0s. - Charles R Greathouse IV, Jan 06 2023
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LINKS
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EXAMPLE
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11 is a term since 1^5 + 1^5 = 2 is prime.
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MATHEMATICA
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top = 999; (* Find all terms <= top *)
For[t = 11, t <= top, t++, k = IntegerLength[t]; sum = 0;
For[e = 0, e <= k - 1, e++, sum = sum + NumberDigit[t, e]^5];
If[PrimeQ[sum] == True, Print[t]]]
Select[Range[670], PrimeQ[Total[IntegerDigits[#]^5]] &] (* Stefano Spezia, Jan 08 2023 *)
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PROG
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(PARI) isok(k) = isprime(vecsum(apply(x->x^5, digits(k)))); \\ Michel Marcus, Jan 07 2023
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CROSSREFS
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Cf. A055014 (sum of the 5th powers of digits).
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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