A079397 Smallest prime with memory = n.

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

Offset: 0

Author

Joseph L. Pe, Feb 16 2003

Keywords

• base
• nice
• nonn

Comments

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

Examples

			113 is the smallest prime with memory = 3. (The smaller primes 3, 11, 13 are substrings of 113.) Hence a(3) = 113.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 0..36 (terms 0-31 from Robert G. Wilson v)

Crossrefs

Cf. A079066, A035244, A035232.

Programs

Mathematica

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 *)

Formula

a(n) > 10^floor((sqrt(8*n+1)-1)/2). - Hieronymus Fischer, Aug 26 2012

a(n) >= min(A035244(k+1), k >= n). - Hieronymus Fischer, Aug 26 2012

Extensions

Edited and extended by Robert G. Wilson v, Feb 25 2003

a(24)-a(27) from Robert G. Wilson v, Aug 03 2010