A080153 a(1)=2, a(2)=3; a(n) for n>2 is the first prime > a(n-1) such that the concatenation of a(n-1), a(n-2) and a(n) is also prime.

2, 3, 11, 23, 31, 41, 59, 79, 97, 107, 113, 151, 163, 179, 197, 223, 227, 241, 257, 271, 337, 383, 433, 439, 467, 491, 547, 619, 773, 797, 853, 883, 887, 911, 967, 977, 1069, 1129, 1187, 1223, 1291, 1297, 1409, 1483, 1489, 1523, 1559, 1567, 1579, 1607, 1619

Offset: 1

Author

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

Keywords

• nonn
• base

Examples

			E.g. a(3) is the smallest prime > a(2)=3 which, when concatenated to 23 (which is the concatenation of a(1) and a(2)) gives a prime. Thus a(3)=11 because 235 and 237 are composite.
		

Crossrefs

Cf. A073640.

Programs

Maple

with(numtheory): pout := [2,3]: nout := [1,2]: for n from 3 to 1000 do: p := ithprime(n): d := parse(cat(pout[nops(pout)-1],pout[nops(pout)],p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: pout;

Mathematica

a[1] = 2; a[2] = 3; a[n_] := a[n] = SelectFirst[Prime@ Range[#, 10^3 + #] &[PrimePi@ a[n - 1] + 1], PrimeQ@ FromDigits@ Join[IntegerDigits@ a[n - 2], IntegerDigits@ a[n - 1], IntegerDigits@ #] &]; Array[a, 51] (* Version 10, or *)
a[1] = 2; a[2] = 3; a[n_] := a[n] = Block[{p = PrimePi@ a[n - 1] + 1},
While[! PrimeQ@ FromDigits@ Join[IntegerDigits@ a[n - 2], IntegerDigits@ a[n - 1], IntegerDigits@ p], p = NextPrime@ p]; p]; Array[a, 51] (* Michael De Vlieger, Aug 15 2016 *)

Extensions

Edited by Charles R Greathouse IV, Apr 26 2010

Edited by Zak Seidov, Aug 15 2016