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%I #10 Mar 01 2022 14:50:59
%S 2,23,313,3137,233347,739397,379837313,73932013313,7399973479337
%N a(n) is the least prime that is the concatenation of two primes in exactly n different ways.
%e 23 = 2 & 3, 313 = 3 & 13 and 31 & 3, etc.
%t f[n_] := Block[{c = 0, id = IntegerDigits@n, k = 0}, len = Length@ id; While[ k < len, If[ Union@ PrimeQ[ FromDigits@# & /@ {id[[;; k + 1]], id[[k + 2 ;;]]}] == {True}, c++ ]; k++ ]; c]; t = Table[0, {10}]; p = 2; While[p < 10^8, a = f@p; If[ t[[a]] == 0, t[[a]] = p; Print[{a, p}]]; p = NextPrime@ p]
%Y Cf. A105184, A106582.
%K base,more,nonn
%O 0,1
%A _Robert G. Wilson v_, Mar 02 2010
%E a(6) from _Robert G. Wilson v_, Mar 04 2010
%E a(7) from _Donovan Johnson_, Nov 09 2010
%E a(8) from _Giovanni Resta_, Mar 04 2014
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