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

1,1

Links

Table of n, a(n) for n=1..51.

Example

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.

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 *)

Crossrefs

Cf. A073640.

Sequence in context: A070174 A320393 A350853 * A040124 A082739 A158017

Adjacent sequences: A080150 A080151 A080152 * A080154 A080155 A080156

Keyword

nonn,base

Author

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

Extensions

Edited by Charles R Greathouse IV, Apr 26 2010

Edited by Zak Seidov, Aug 15 2016

Status

approved