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

1,1

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".

Links

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

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.

Example

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.

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]

Crossrefs

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

Cf. A033679, A069603, A074338.

Sequence in context: A038987 A142957 A191058 * A235625 A032357 A144056

Adjacent sequences: A080152 A080153 A080154 * A080156 A080157 A080158

Keyword

nonn,base

Author

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

Status

approved