This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091365 #6 Jun 08 2025 16:15:42
%S A091365 997,2797,3499,4993,7297,7477,7927,8089,8999,9277,9349,9439,9907,
%T A091365 11689,12697,12967,14479,14767,14929,14947,16189,16477,16729,16747,
%U A091365 16927,16981,17449,17467,18169,18691,19249,19267,19429,19447,19681,19861
%N 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.
%C A091365 Apparently if the cubes of the digits of a prime sum to a prime, it is more likely that the digits themselves also sum to a prime. In the first 10,000 primes there are 1969 primes p such that the cubes of the digits of p sum to a prime. Of these, only 358 are such that the sums of the digits are not prime. Interestingly, all of these primes have a digit sum of 25 or 35. Essentially this sequence is the terms of A091366 (primes whose digits cubed sum to a prime) that do not also appear in A046704 (primes whose digits sum to a prime).
%H A091365 Vincenzo Librandi, <a href="/A091365/b091365.txt">Table of n, a(n) for n = 1..1000</a>
%e A091365 a(1)=997 because 9+9+7 = 25 which is not prime, but 9^3+9^3+7^3 = 1801 which is prime.
%t A091365 ssdQ[n_]:= Module[{idn = IntegerDigits[n]}, !PrimeQ[Total[idn]]&&PrimeQ[Total[idn^3]]]; Select[Prime[Range[4000]], ssdQ] (* _Vincenzo Librandi_, Apr 17 2013 *)
%Y A091365 Cf. A046704 (primes whose digits sum to a prime) A091366 (primes whose digits squared sum to a prime).
%K A091365 base,nonn
%O A091365 1,1
%A A091365 _Chuck Seggelin_, Jan 03 2004