A192610 Numbers k such that the concatenation of k^3 k^2 k^1 k^0 is prime.

9, 36, 37, 54, 55, 76, 79, 330, 333, 352, 370, 394, 405, 417, 427, 456, 490, 492, 498, 504, 517, 550, 583, 624, 634, 652, 667, 762, 795, 828, 855, 874, 876, 891, 898, 903, 921, 924, 925, 930, 949, 960, 967, 982, 3181, 3186, 3201, 3208, 3232, 3243, 3274, 3333, 3336, 3402, 3403, 3409, 3411, 3442

Offset

1,1

Comments

All terms == 0 or 1 (mod 3). - Robert Israel, May 20 2026

Links

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

Example

9 is in the list because the concatenation of 9^3 9^2 9^1 9^0 is 7298191 and this number is prime.

Maple

lcat:= proc(L) local x, i;
  x:= L[1];
  for i from 2 to nops(L) do
    x:= x*10^(1+ilog10(L[i]))+L[i]
  od;
  x
end proc:
filter:= n -> isprime(lcat([n^3, n^2, n, 1])):
select(filter, [$1..5000]); # Robert Israel, May 20 2026

Mathematica

Select[Range[1000], PrimeQ[FromDigits[Flatten[IntegerDigits/@ (#^Range[ 3, 0, -1])]]]&] (* Harvey P. Dale, Jul 27 2011 *)

Crossrefs

Cf. A192608, A192609.

Sequence in context: A330907 A231666 A143224 * A319958 A329808 A169580

Adjacent sequences: A192607 A192608 A192609 * A192611 A192612 A192613

Keyword

nonn,base

Author

Claudio Meller, Jul 05 2011

Extensions

More terms from Robert Israel, May 20 2026

Status

approved