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%I #39 Jun 14 2018 02:23:19
%S 2,13,23,113,137,1237,1733,1373,12373,11317,23719,111317,113171,
%T 211373,1131379,1113173,1317971,2313797,11131733,11373379,23931379,
%U 113193797,52313797,129733313,113733797,523137971,1113179719,1317971939
%N Smallest prime with memory = n.
%C The memory of a prime p is the number of previous primes contained as substrings in (the decimal representation of) p.
%C Also the minimal prime such that the number of different prime substrings is n+1 (substrings with leading zeros are considered to be nonprime). - _Hieronymus Fischer_, Aug 26 2012
%H Hieronymus Fischer, <a href="/A079397/b079397.txt">Table of n, a(n) for n = 0..36</a> (terms 0-31 from Robert G. Wilson v)
%F a(n) > 10^floor((sqrt(8*n+1)-1)/2). - _Hieronymus Fischer_, Aug 26 2012
%F a(n) >= min(A035244(k+1), k >= n). - _Hieronymus Fischer_, Aug 26 2012
%e 113 is the smallest prime with memory = 3. (The smaller primes 3, 11, 13 are substrings of 113.) Hence a(3) = 113.
%t f[n_] := Block[{id = IntegerDigits@n}, len = Length@id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[id, k, 1], {k, len}], 1]], True] + 1]; t = Table[0, {30}]; p = 2; While[p < 11500000000, a = f@p; If[t[[a]] == 0, pp = PrimePi@p; t[[a]] = pp; Print[{a, p, pp}]]; p = NextPrime@p]; t (* _Robert G. Wilson v_, Aug 03 2010 *)
%Y Cf. A079066, A035244, A035232.
%K base,nice,nonn
%O 0,1
%A _Joseph L. Pe_, Feb 16 2003
%E Edited and extended by _Robert G. Wilson v_, Feb 25 2003
%E a(24)-a(27) from _Robert G. Wilson v_, Aug 03 2010
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