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A245475
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Numbers n such that the sum of digits, sum of squares of digits, and sum of cubes of digits are all prime.
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0
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11, 101, 110, 111, 113, 131, 146, 164, 166, 199, 223, 232, 289, 298, 311, 322, 335, 337, 346, 353, 355, 364, 373, 388, 416, 436, 449, 461, 463, 494, 533, 535, 553, 566, 614, 616, 634, 641, 643, 656, 661, 665, 733, 829, 838, 883, 892, 919, 928, 944, 982, 991, 1001, 1010, 1011, 1013, 1031, 1046, 1064, 1066, 1099
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OFFSET
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1,1
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COMMENTS
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There are infinitely many numbers in this sequence; 0's can be added to any number any number of times in any logical order (i.e., the number doesn't start with a zero).
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LINKS
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EXAMPLE
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1^1 + 4^1 + 6^1 = 11 is prime.
1^2 + 4^2 + 6^2 = 53 is prime.
1^3 + 4^3 + 6^3 = 281 is prime.
Thus 146, 164, 416, 461, 641, and 614 are members of this sequence.
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MATHEMATICA
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sdpQ[n_]:=Module[{idn=IntegerDigits[n]}, AllTrue[{Total[idn], Total[ idn^2], Total[ idn^3]}, PrimeQ]]; Select[Range[1100], sdpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 06 2018 *)
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PROG
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(PARI) for(n=1, 10^3, d=digits(n); s1=sum(i=1, #d, d[i]); s2=sum(j=1, #d, d[j]^2); s3=sum(k=1, #d, d[k]^3); if(isprime(s1)&&isprime(s2)&&isprime(s3), print1(n, ", ")))
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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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