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A245193 Smallest prime having in decimal representation A136333(n) as suffix.

%I A245193 #16 Feb 25 2022 10:30:35
%S A245193 11,3,7,19,11,13,17,19,31,233,37,139,71,73,277,79,191,193,97,199,2111,
%T A245193 113,1117,3119,131,4133,137,139,1171,173,4177,179,191,193,197,199,311,
%U A245193 313,317,1319,331,2333,337,2339,2371,373,2377,379,3391,2393,397,1399
%N A245193 Smallest prime having in decimal representation A136333(n) as suffix.
%C A245193 a(n) = A136333(n) iff A136333(n) itself is a prime number, cf. A091633.
%H A245193 Reinhard Zumkeller, <a href="/A245193/b245193.txt">Table of n, a(n) for n = 1..1000</a>
%e A245193 .    n  |   a(n)  | A136333(n)
%e A245193 . ------+---------+-----------
%e A245193 .   10  |    233  |      33
%e A245193 .   11  |     37  |      37
%e A245193 .   12  |    139  |      39
%e A245193 .   13  |     71  |      71
%e A245193 .   14  |     73  |      73
%e A245193 .   15  |    277  |      77
%e A245193 .   16  |     79  |      79
%e A245193 .   17  |    191  |      91
%e A245193 .   18  |    193  |      93
%e A245193 .   19  |     97  |      97
%e A245193 .   20  |    199  |      99
%e A245193 .   21  |   2111  |     111
%e A245193 .   22  |    113  |     113
%e A245193 .   23  |   1117  |     117
%e A245193 .   24  |   3119  |     119
%e A245193 .   25  |    131  |     131
%e A245193 .   26  |   4133  |     133
%e A245193 .   27  |    137  |     137
%e A245193 .   28  |    139  |     139
%e A245193 .   29  |   1171  |     171
%e A245193 .   30  |    173  |     173 .
%o A245193 (Haskell)
%o A245193 import Data.List (isSuffixOf); import Data.Function (on)
%o A245193 a245193 n = head [p | p <- a000040_list,
%o A245193                       (isSuffixOf `on` show) (a136333 n) p]
%o A245193 (PARI) isok(m) = my(d=digits(m)); apply(x->gcd(x, 10), d) == vector(#d, k, 1); \\ A136333
%o A245193 f(m) = my(p=nextprime(m), s=10^#Str(m)); while ((p-m) % s, p = nextprime(p+1)); p;
%o A245193 lista(nn) = apply(x->f(x), select(isok, [1..nn]));
%o A245193 lista(1000) \\ _Michel Marcus_, Feb 25 2022
%Y A245193 Cf. A000040, A091633, A136333.
%K A245193 nonn,base
%O A245193 1,1
%A A245193 _Reinhard Zumkeller_, Jul 18 2014