A384953 First of three consecutive primes whose concatenations, both forward and backward, are primes.

313, 359, 383, 449, 619, 787, 827, 907, 1697, 2503, 2521, 2857, 3673, 3853, 4139, 4363, 4993, 5281, 5527, 5563, 5641, 5851, 6037, 6043, 6719, 7019, 7477, 9281, 10177, 10459, 13799, 14009, 15013, 15511, 17167, 17209, 19183, 19423, 20483, 20743, 21397, 21407, 25111

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 383 is a term because 383, 389 and 397 are consecutive primes and both 383389397 and 397389383 are prime.

Maple

rcat:= proc(L) local x, i;
  x:= L[1];
  for i from 2 to nops(L) do
    x:= 10^(1+ilog10(x))*L[i] + x
  od;
  x
end proc:
fcat:= proc(L) local x, i;
  x:= L[1];
  for i from 2 to nops(L) do
    x:= 10^(1+ilog10(L[i]))*x + L[i]
  od;
  x
end proc:
P:= select(isprime, [seq(i, i=3..30000, 2)]):
J:=  select(i -> isprime(rcat(P[i..i+2])) and isprime(fcat(P[i..i+2])), [$1..nops(P)-2]):
P[J];

Crossrefs

Cf. A030469, A104328.

Sequence in context: A088282 A068687 A093808 * A383815 A257527 A142745

Adjacent sequences: A384950 A384951 A384952 * A384954 A384955 A384956

Keyword

nonn,base

Author

Robert Israel, Jun 13 2025

Status

approved