A110772 Beginning with 2, least number not occurring earlier such that every partial concatenation is prime.

2, 3, 9, 11, 13, 63, 51, 29, 69, 33, 49, 159, 17, 37, 39, 117, 53, 43, 47, 31, 23, 97, 171, 89, 367, 347, 157, 83, 447, 19, 249, 153, 233, 163, 141, 317, 471, 391, 107, 93, 261, 339, 183, 87, 403, 129, 81, 173, 411, 57, 177, 109, 71, 121, 269, 609, 111, 1413, 99, 21

Offset: 1

Author

Amarnath Murthy, Aug 12 2005

Keywords

• easy
• nonn
• base

Comments

Conjecture: every odd number not divisible by 5 is a member.

Examples

			2, 23, 239, 23911, 2391113, ... etc. are all prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1078

Crossrefs

Cf. A089564, A110773.

Programs

Maple

L:=[2]: for n from 1 to 120 do for m from 1 do if isprime(parse(cat("",op(L),m))) and not member(m,L) then L:=[op(L),m]; break fi od od: L[]; # Alec Mihailovs, Aug 14 2005

Mathematica

a[1]=2;a[n_]:=a[n]=Block[{t=1},While[!PrimeQ[FromDigits@Flatten[IntegerDigits/@Join[Array[a,n-1],{t}]]]||MemberQ[Array[a,n-1],t],t++];t];Array[a,60] (* Giorgos Kalogeropoulos, May 07 2023 *)

Python

from gmpy2 import is_prime
from itertools import count, islice
def agen(): # generator of terms
    an, s, aset, mink = 2, "2", {2}, 3
    while True:
        yield an
        an = next(k for k in count(mink, 2) if k not in aset and is_prime(int(s+str(k))))
        s += str(an)
        aset.add(an)
        while mink in aset: mink += 2
print(list(islice(agen(), 60))) # Michael S. Branicky, May 11 2023

Extensions

More terms from Alec Mihailovs (alec(AT)mihailovs.com), Aug 14 2005

Edited by Charles R Greathouse IV, Apr 27 2010