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.

3, 23, 223, 31223, 231223, 31231223, 2931231223, 372931231223, 17372931231223, 1317372931231223, 1971317372931231223, 1571971317372931231223, 891571971317372931231223, 79891571971317372931231223, 25179891571971317372931231223, 4325179891571971317372931231223

Offset: 1

Author

Michel Lagneau, Dec 27 2011

Keywords

• nonn
• base

Comments

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]

Examples

			a(1) = 3;
a(2) = 23 because 2 is the smallest prime prefix and 23 is prime;
a(3) = 223 because 2 is the smallest prime prefix and 223 is prime;
a(4) = 31223 because 31 is the smallest prime prefix and 31223 is prime.
		

Crossrefs

Cf. A173291, A379354, A379355, A379782.

Programs

Maple

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: