A073640 a(1) = 2; a(n) = smallest prime greater than the previous term such that concatenation of two successive terms is a prime.

2, 3, 7, 19, 31, 37, 61, 73, 127, 139, 199, 211, 229, 283, 397, 433, 439, 463, 523, 541, 547, 577, 601, 607, 619, 739, 751, 787, 811, 919, 937, 991, 1009, 1021, 1039, 1093, 1201, 1213, 1297, 1447, 1453, 1459, 1471, 1483, 1657, 1663, 1723, 1783, 1867, 1879

Offset: 1

Author

Amarnath Murthy, Aug 09 2002

Keywords

• base
• nonn

Comments

All terms after 3 must have the form 6k + 1. - Mauro Fiorentini, Mar 27 2024

Examples

			a(1)=2, the next prime is 3 and when 2 and 3 are concatenated we get 23, another prime. Hence a(2)=3. Likewise, a(3)=7 because 37 is prime, whereas the next prime after 3 is "5" which would lead to the nonprime "35".
		

Programs

Maple

pout := [2]: nout := [1]: for n from 2 to 1000 do: p := ithprime(n): d := parse(cat(pout[nops(pout)],p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od:

Mathematica

t = {i = 2}; Do[While[! PrimeQ[FromDigits[Flatten[IntegerDigits[{Last[t], x = Prime[i]}]]]], i++]; AppendTo[t, x], {49}]; t (* Jayanta Basu, Jul 03 2013 *)

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003