A121642 Numbers with composite sum of digits and prime sum of cubes of digits.
799, 889, 898, 979, 988, 997, 2779, 2797, 2977, 3499, 3949, 3994, 4399, 4588, 4777, 4858, 4885, 4939, 4993, 5488, 5668, 5686, 5848, 5866, 5884, 6568, 6586, 6658, 6667, 6676, 6685, 6766, 6856, 6865, 7099, 7279, 7297, 7477, 7666, 7729, 7747, 7774, 7792
Offset: 1
Examples
For example the sum of digits of 799 is 25 which is composite; the sum of the cubes of its digits is 343 + 729 + 729 = 1801, which is prime.
Crossrefs
Cf. A091365 (Primes p such that the sum of the digits of p is not prime, but the sum of the cubes of the digits of p is prime.) is a subsequence of this sequence.
Programs
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Mathematica
sod[k_, m_] := Plus @@ (IntegerDigits[k]^m); Select[ Table[n, {n, 10000}], (! PrimeQ[sod[ #, 1]] && PrimeQ[sod[ #, 3]]) &]