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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

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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