A309191 a(n) is the least prime such that each concatenation of 1 <= k <= n consecutive primes beginning with a(n) is prime, or 0 if no such prime exists.

2, 2, 31, 4603, 910307, 352367441, 23908162969, 483148266971

Offset: 1

Author

Jean-Marc Rebert, Jul 16 2019

Keywords

• nonn
• base
• more

Examples

			a(2)=2; 2, 3 are 2 consecutive primes and their concatenation 23 is also prime.
a(3)=31 since 31, 37, and 41 are 3 consecutive primes and 3137 and 313741 are both prime.
		

Links

• Carlos Rivera, Puzzle 708. Find sets of k consecutive primes such that ..., The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A030996.

Programs

Mathematica

a[n_] := Block[{p = Prime@ Range@ n}, While[! AllTrue[Range[2, n], PrimeQ@ FromDigits@ Flatten@ IntegerDigits@ Take[p, #] &], p = Append[ Rest@ p, NextPrime@ Last@ p]]; p[[1]]]; Array[a, 5] (* Giovanni Resta, Jul 16 2019 *)