A384958 - OEIS

%I #8 Jun 14 2025 00:20:25

%S 2,199,313,139,67,113,163,1583,23789,941,131,5351,26801,2693,4073,

%T 15859,4919,23209,176053,86783,29717,20849,151289,50111,51971,23689,

%U 11807,180337,563,25153,517381,36313,256121,753091,208441,28573,4049,108943,451361,114343,28447,21001,4001,3137,6833,885919

%N 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.

%H Robert Israel, <a href="/A384958/b384958.txt">Table of n, a(n) for n = 1..135</a>

%e 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.

%p rcat:= proc(L) local x,i;

%p   x:= L[1];

%p   for i from 2 to nops(L) do

%p     x:= 10^(1+ilog10(x))*L[i] + x

%p   od;

%p   x

%p end proc:

%p fcat:= proc(L) local x,i;

%p   x:= L[1];

%p   for i from 2 to nops(L) do

%p     x:= 10^(1+ilog10(L[i]))*x + L[i]

%p   od;

%p   x

%p end proc:

%p f:= proc(n) local L,i;

%p      L:= [0,seq(ithprime(i),i=1..n-1)];

%p      do

%p        L:= [op(L[2..-1]),nextprime(L[-1])];

%p        if isprime(fcat(L)) and isprime(rcat(L)) then return L[1] fi

%p      od

%p end proc:

%p map(f, [$1..50]);

%Y Cf. A384953.

%K nonn,base

%O 1,1

%A _Robert Israel_, Jun 13 2025