A384958 a(n) is the first prime p such that the concatenations of n consecutive primes, starting with p, in both forward and backward directions, are prime.

2, 199, 313, 139, 67, 113, 163, 1583, 23789, 941, 131, 5351, 26801, 2693, 4073, 15859, 4919, 23209, 176053, 86783, 29717, 20849, 151289, 50111, 51971, 23689, 11807, 180337, 563, 25153, 517381, 36313, 256121, 753091, 208441, 28573, 4049, 108943, 451361, 114343, 28447, 21001, 4001, 3137, 6833, 885919

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..135

Example

a(4) = 139 because the four consecutive primes starting with 139 are 139, 149, 151, 157, both 139149151157 and 157151149139 are prime, and no smaller prime works.

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:
f:= proc(n) local L, i;
     L:= [0, seq(ithprime(i), i=1..n-1)];
     do
       L:= [op(L[2..-1]), nextprime(L[-1])];
       if isprime(fcat(L)) and isprime(rcat(L)) then return L[1] fi
     od
end proc:
map(f, [$1..50]);

Crossrefs

Cf. A384953.

Sequence in context: A123100 A383322 A033147 * A213162 A124339 A089772

Adjacent sequences: A384955 A384956 A384957 * A384959 A384960 A384961

Keyword

nonn,base

Author

Robert Israel, Jun 13 2025

Status

approved