A245475 Numbers n such that the sum of digits, sum of squares of digits, and sum of cubes of digits are all prime.

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

Offset

1,1

Comments

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).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

filter:= proc(n) local L;
  L:= convert(n, base, 10);
  isprime(convert(L, `+`)) and
  isprime(convert(map(`^`, L, 2), `+`)) and
  isprime(convert(map(`^`, L, 3), `+`))
end proc:
select(filter, [$1..2000]); # Robert Israel, Dec 04 2024

Mathematica

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A182404, A225534, A108662.

Sequence in context: A292451 A292731 A225534 * A175963 A359610 A239236

Adjacent sequences: A245472 A245473 A245474 * A245476 A245477 A245478

Keyword

nonn,base

Author

Derek Orr, Jul 23 2014

Status

approved