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

1,1

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).

Links

Table of n, a(n) for n=1..36.

Example

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.

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;

Crossrefs

Cf. A010784, A356196.

Sequence in context: A181260 A316482 A340897 * A228299 A178279 A097239

Adjacent sequences: A371351 A371352 A371353 * A371355 A371356 A371357

Keyword

nonn,fini,full,base

Author

Zak Seidov and Robert Israel, Mar 19 2024

Status

approved