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A088629 Smallest number k not included earlier such that the concatenation n, k is a prime.

%I A088629 #12 Aug 20 2022 13:37:47
%S A088629 1,3,7,19,9,13,27,11,29,21,17,23,61,33,31,37,41,47,49,39,43,51,57,59,
%T A088629 79,63,53,87,69,67,81,71,73,91,83,77,93,89,103,99,113,97,117,101,119,
%U A088629 133,111,109,121,123,131,127,129,139,147,149,107,151,141,161,153,137,179
%N A088629 Smallest number k not included earlier such that the concatenation n, k is a prime.
%C A088629 Another rearrangement of odd numbers not == 0 (mod 5).
%H A088629 Michael S. Branicky, <a href="/A088629/b088629.txt">Table of n, a(n) for n = 1..10000</a>
%e A088629 a(4) = 19. Though 41, 43 and 47 are prime 1, 3 and 7 have been included earlier and also 49, 411, 413 and 417 are not prime hence 419 is the required prime.
%o A088629 (Python)
%o A088629 from sympy import isprime
%o A088629 from itertools import count, islice
%o A088629 def agen():
%o A088629     aset, mink = set(), 1
%o A088629     for n in count(1):
%o A088629         s, k = str(n), mink
%o A088629         while k in aset or not isprime(int(s + str(k))): k += 1
%o A088629         while mink%5 == 0 or mink in aset: mink += 2
%o A088629         yield k; aset.add(k)
%o A088629 print(list(islice(agen(), 63))) # _Michael S. Branicky_, Aug 20 2022
%Y A088629 Cf. A045572, A088630.
%K A088629 base,nonn
%O A088629 1,2
%A A088629 _Amarnath Murthy_, Oct 21 2003
%E A088629 More terms from _Ray G. Opao_, Aug 19 2004