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A110772
Beginning with 2, least number not occurring earlier such that every partial concatenation is prime.
3
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
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
Sequence in context: A272537 A121557 A138984 * A074338 A111319 A109658
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