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A079397
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Smallest prime with memory = n.
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43
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2, 13, 23, 113, 137, 1237, 1733, 1373, 12373, 11317, 23719, 111317, 113171, 211373, 1131379, 1113173, 1317971, 2313797, 11131733, 11373379, 23931379, 113193797, 52313797, 129733313, 113733797, 523137971, 1113179719, 1317971939
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OFFSET
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0,1
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COMMENTS
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The memory of a prime p is the number of previous primes contained as substrings in (the decimal representation of) p.
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
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LINKS
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FORMULA
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EXAMPLE
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113 is the smallest prime with memory = 3. (The smaller primes 3, 11, 13 are substrings of 113.) Hence a(3) = 113.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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base,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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