A080155 a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.

2, 3, 11, 31, 47, 229, 251, 577, 857, 859, 911, 1123, 1223, 1297, 1571, 2161, 2417, 2551, 2879, 3319, 5273, 6121, 6947, 7603, 8273, 12721, 12953, 13291, 15683, 16453, 17207, 18133, 20399, 23743, 23909, 25849, 28277, 28879, 35291, 35461, 36107, 43573

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

See A073640 for the sequence involving concatenation of 2 successive terms, A080153 for 3 successive terms. Primeness is established using Maple's isprime() function, so later terms should be regarded as "probable".

Examples

			E.g. a(5)=47 since this is the smallest prime>a(4) which, when concatenated with the concatenation of a(1) to a(4) (=231131), also yields a prime, in this case 23113147.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..201

Crossrefs

Cf. A073640, A080152, A080153, A080154, A080156.

Cf. A033679, A069603, A074338.

Programs

Maple

with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i],i=1..nops(pout)),p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: pout;

Mathematica

f[s_List] := Block[{p=NextPrime@s[[-1]], pp=FromDigits@Flatten[IntegerDigits/@s]}, While[!PrimeQ[pp*10^Floor[Log[10,p]+1]+p], p=NextPrime@p]; Append[s,p]]; Nest[f,{2},40]

Formula

For any n>1, a(n) is prime and a(n) > a(n-1). a(n) is the smallest prime for which a(1)//a(2)//...//a(n) is prime. // denotes concatenation.