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

%I A110772 #18 May 11 2023 12:47:29
%S A110772 2,3,9,11,13,63,51,29,69,33,49,159,17,37,39,117,53,43,47,31,23,97,171,
%T A110772 89,367,347,157,83,447,19,249,153,233,163,141,317,471,391,107,93,261,
%U A110772 339,183,87,403,129,81,173,411,57,177,109,71,121,269,609,111,1413,99,21
%N A110772 Beginning with 2, least number not occurring earlier such that every partial concatenation is prime.
%C A110772 Conjecture: every odd number not divisible by 5 is a member.
%H A110772 Michael S. Branicky, <a href="/A110772/b110772.txt">Table of n, a(n) for n = 1..1078</a>
%e A110772 2, 23, 239, 23911, 2391113, ... etc. are all prime.
%p A110772 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
%t A110772 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 *)
%o A110772 (Python)
%o A110772 from gmpy2 import is_prime
%o A110772 from itertools import count, islice
%o A110772 def agen(): # generator of terms
%o A110772     an, s, aset, mink = 2, "2", {2}, 3
%o A110772     while True:
%o A110772         yield an
%o A110772         an = next(k for k in count(mink, 2) if k not in aset and is_prime(int(s+str(k))))
%o A110772         s += str(an)
%o A110772         aset.add(an)
%o A110772         while mink in aset: mink += 2
%o A110772 print(list(islice(agen(), 60))) # _Michael S. Branicky_, May 11 2023
%Y A110772 Cf. A089564, A110773.
%K A110772 easy,nonn,base
%O A110772 1,1
%A A110772 _Amarnath Murthy_, Aug 12 2005
%E A110772 More terms from Alec Mihailovs (alec(AT)mihailovs.com), Aug 14 2005
%E A110772 Edited by _Charles R Greathouse IV_, Apr 27 2010