A079066 "Memory" of prime(n): the number of distinct (previous) primes contained as substrings in prime(n).

0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 0, 3, 2, 3, 4, 2, 0, 1, 2, 1, 2, 4, 3, 0, 1, 2, 3, 1, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 1, 3, 2, 1, 3, 3, 2, 3, 3, 4, 2, 3, 3, 1, 3, 3, 3, 4, 4, 2, 2, 3, 0, 0, 2, 1, 3, 2, 2, 2, 0, 2, 1, 1, 2, 3, 1, 0, 0, 2, 1, 2, 4, 2, 3, 2, 2, 1, 3

Offset

1,9

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A039997(prime(n)) - 1.

a(n) = A039996(n) - 1. - Alois P. Heinz, Jul 29 2025

Example

The primes contained as substrings in prime(3) = 113 are 3, 11, 13. Hence a(30) = 3. 113 is the smallest prime with memory = 3.

Maple

a:= n-> (s-> -1+nops(select(t -> t[1]<>"0" and isprime(parse(t)),
        {seq(seq(s[i..j], i=1..j), j=1..length(s))})))(""||(ithprime(n))):
seq(a(n), n=1..105);  # Alois P. Heinz, Jul 29 2025

Mathematica

ub = 105; tprime = Table[ToString[Prime[i]], {i, 1, ub}]; a = {}; For[i = 1, i <= ub, i++, m = 0; For[j = 1, j < i, j++, If[Length[StringPosition[tprime[[i]], tprime[[j]]]] > 0, m = m + 1]]; a = Append[a, m]]; a

Prog

(Haskell)
import Data.List (isInfixOf)
a079066 n =
   length $ filter (`isInfixOf` (primesDec !! n)) $ take n primesDec
primesDec = "_" : map show a000040_list
-- Reinhard Zumkeller, Jul 19 2011

Crossrefs

Cf. A079075, A035232, A039996, A039997.

Cf. A033274, A179909, A179910, A179911, A179912, A179913, A179914, A179915, A179916, A179917, A179918, A179919, A179922.

Sequence in context: A240857 A374318 A109066 * A392157 A157188 A329257

Adjacent sequences: A079063 A079064 A079065 * A079067 A079068 A079069

Keyword

base,easy,nonn

Author

Joseph L. Pe, Feb 02 2003

Extensions

Edited by Robert G. Wilson v, Feb 25 2003

Name clarified by Sean A. Irvine, Jul 29 2025

Status

approved