A371354 Primes p such that p, q and p + q but not q - p have distinct digits, where q is the next prime after p.

21067, 46279, 46831, 47659, 62017, 124853, 241567, 347629, 410257, 428093, 456901, 476059, 528719, 638179, 685471, 789631, 869521, 1024357, 2014357, 2146853, 2354167, 3268549, 3407659, 3682457, 3825649, 4021357, 4026571, 4180679, 4213567, 4562791, 7685401, 8602417, 20418637, 41870293, 76820453, 390465721

Offset: 1

Author

Zak Seidov and Robert Israel, Mar 19 2024

Keywords

• nonn
• fini
• full
• base

Comments

Primes p = prime(k) such that p, prime(k+1) and p + prime(k+1) are in A010784 but p is not in A356196 (as prime(k+1) - p is not in A010784).

Examples

			a(3) = 46831 is a term because it is prime, the next prime is 46853, and 46831, 46853 and 46831 + 46853 = 93684 have distinct digits but 46853 - 46831 = 22 does not.
		

Crossrefs

Cf. A010784, A356196.

Programs

Maple

isdd:= proc(n) local L;
  L:= convert(n,base,10);
  nops(L) = nops(convert(L,set))
end proc:
Res:= NULL:
for d from 1 to 9 do
  for t in combinat:-permute([$0..9],d) do
    if t[1] = 0 then next fi;
    p:= add(t[i]*10^(d-i),i=1..d);
    if isprime(p) then
      q:= nextprime(p);
      if not(isdd(q-p)) and isdd(q) and isdd(p+q) then
         Res:= Res,p;
      fi
    fi
od od:
Res;