cp's OEIS Frontend

A202997 a(1) = 3 ; a(n+1) is the prime number obtained by the concatenation {p, a(n)} where p is the smallest prime prefix.

%I A202997 #17 Jan 03 2025 01:57:11
%S A202997 3,23,223,31223,231223,31231223,2931231223,372931231223,
%T A202997 17372931231223,1317372931231223,1971317372931231223,
%U A202997 1571971317372931231223,891571971317372931231223,79891571971317372931231223,25179891571971317372931231223,4325179891571971317372931231223
%N A202997 a(1) = 3 ; a(n+1) is the prime number obtained by the concatenation {p, a(n)} where p is the smallest prime prefix.
%C A202997 By Xylouris' version of Linnik's theorem, a(n) << 3^(6.2^n + cn) for some constant c. [_Charles R Greathouse IV_, Dec 27 2011]
%e A202997 a(1) = 3;
%e A202997 a(2) = 23 because 2 is the smallest prime prefix and 23 is prime;
%e A202997 a(3) = 223 because 2 is the smallest prime prefix and 223 is prime;
%e A202997 a(4) = 31223 because 31 is the smallest prime prefix and 31223 is prime.
%p A202997 a0:=3: printf(`%d, `,a0):for it from 1 to 20 do: i:=0:for n from 1 to 1000 while(i=0)  do:p0:=ithprime(n):n0:=length(a0):x:=p0*10^n0+a0: if type(x,prime)=true then printf(`%d, `,x):i:=1:a0:=x:else fi:od:od:
%Y A202997 Cf. A173291, A379354, A379355, A379782.
%K A202997 nonn,base
%O A202997 1,1
%A A202997 _Michel Lagneau_, Dec 27 2011