A350853 a(1) = 2, a(2) = 3; a(n) is the smallest prime not included earlier such that concatenation of three successive terms is a prime.

2, 3, 11, 23, 31, 13, 29, 7, 17, 19, 37, 41, 59, 79, 67, 107, 47, 61, 43, 113, 71, 109, 89, 53, 157, 97, 83, 101, 73, 173, 131, 223, 149, 127, 197, 137, 373, 139, 167, 163, 179, 151, 191, 193, 241, 317, 211, 229, 281, 103, 227, 233, 283, 251

Offset: 1

Author

Haines Hoag, Jan 18 2022

Keywords

• nonn
• base

Comments

Not a permutation of the primes. 5 never appears, since numbers m mod 10 = 5 are divisible by 5, and concatenation of 2 previous terms and 5 guarantee a composite number. - Michael De Vlieger, Feb 16 2022

Examples

			From _Michael De Vlieger_, Feb 16 2022: (Start)
a(3) = 11 since 235 and 237 are composite, but 2311 is prime.
a(4) = 23 since 3115, 3117, 31113, 31117, and 31119 are composite, but 31123 is prime.
a(5) = 31 since 11235, 11237, 112313, 112317, 112319, and 112329 are composite, but 112331 is prime. (End)
		

Links

• Haines Hoag, Table of n, a(n) for n = 1..31499
• Michael De Vlieger, Scatterplot of a(n) for n = 1..2^14, showing records in red and local minima (aside from q = 5, which never appears) in blue.

Crossrefs

Cf. A073641, A000040.

Programs

Mathematica

a[1]=2; a[2]=3; a[n_]:=a[n]=(k=2; While[!PrimeQ[FromDigits@Join[Flatten[IntegerDigits/@{a[n-2],a[n-1]}],IntegerDigits@k]]||MemberQ[Array[a,n-1],k],k=NextPrime@k];k);Array[a,54] (* Giorgos Kalogeropoulos, Jan 19 2022 *)