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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A089564, A110773.

Sequence in context: A272537 A121557 A138984 * A074338 A111319 A109658

Adjacent sequences: A110769 A110770 A110771 * A110773 A110774 A110775

Keyword

easy,nonn,base

Author

Amarnath Murthy, Aug 12 2005

Extensions

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

Edited by Charles R Greathouse IV, Apr 27 2010

Status

approved