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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 30 02:06 EDT 2022. Contains 354913 sequences. (Running on oeis4.)