A342299 Lesser of twin primes p,p+2 such that the absolute difference of p and the reverse of p+2 is a twin prime and the absolute difference of p+2 and the reverse of p is a twin prime.

41, 281, 827, 857, 2081, 2801, 8087, 20981, 21191, 21491, 81197, 88607, 206411, 225941, 227531, 233141, 249131, 255971, 261971, 279551, 283571, 825107, 827537, 828407, 834857, 857567, 861977, 864047, 869777, 879167, 883577, 895787, 2051111, 2125601, 2128601, 2130701, 2141801, 2147021, 2163221

Offset

1,1

Comments

Lesser of twin primes p such that both p and p+2 are in A342216.

Except for the first term, all terms either start with 2 and end with 1 or start with 8 and end with 7.

Links

Robert Israel, Table of n, a(n) for n = 1..4327

Example

a(3) = 827 is a term because 827 and 829 are twin primes, and |827-928| = 101 and |827-728| = 101, and 101 is a twin prime.
a(5) = 2081 is a term because 2081 and 2083 are twin primes, and |2081-3802| = 1721 and |2083-1802| = 281 are twin primes.

Maple

digrev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(10^(i-1)*L[-i], i=1..nops(L))
end proc:
filter:= proc(p) local q, t, s;
  if not isprime(p) then return false fi;
  q:= p+2;
  if not isprime(q) then return false fi;
  t:= abs(p - digrev(q));
  s:= abs(q - digrev(p));
  isprime(t) and isprime(s) and (isprime(t-2) or isprime(t+2)) and (isprime(s-2) or isprime(s+2))
end proc:
select(filter, [seq(i, i=5..10^7, 6)]);

Crossrefs

Cf. A004086, A001097, A001359, A342216.

Sequence in context: A180475 A142768 A140013 * A167741 A074281 A090833

Adjacent sequences: A342296 A342297 A342298 * A342300 A342301 A342302

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Mar 07 2021

Status

approved