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A079066
"Memory" of prime(n): the number of (previous) primes contained as substrings in prime(n).
17
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
FORMULA
a(n) = A039997(prime(n)) - 1.
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.
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
KEYWORD
base,easy,nonn
AUTHOR
Joseph L. Pe, Feb 02 2003
EXTENSIONS
Edited by Robert G. Wilson v, Feb 25 2003
STATUS
approved