A114897 - OEIS

A114897

a(1) = 1. a(n+1) = number of earlier terms a(k) (1 <= k <= n) where a(k)+n is a prime.

1, 1, 2, 1, 3, 1, 4, 1, 1, 2, 7, 2, 7, 1, 1, 4, 11, 3, 9, 2, 4, 4, 11, 0, 2, 4, 4, 11, 11, 6, 14, 2, 5, 7, 6, 8, 16, 10, 4, 15, 13, 9, 13, 10, 5, 9, 14, 5, 9, 9, 11, 10, 17, 6, 9, 11, 13, 19, 20, 11, 22, 8, 17, 14, 13, 14, 20, 13, 13, 22, 23, 9, 20, 8, 12, 16, 11, 13, 21, 13, 13, 16, 14, 12

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OFFSET

1,3

LINKS

T. D. Noe, Table of n, a(n) for n=1..2000

FORMULA

a(n) = A123541(n-1) for n>3. - T. D. Noe, Apr 29 2007

EXAMPLE

If we add 10 to each of the first 10 terms of the sequence, we get

[11,11,12,11,13,11,14,11,11,12]. Of these only the six 11's and the 13 are primes. So a(11) = 7.

MATHEMATICA

a[1] = 1; a[n_] := a[n] = (For[k = 1; cnt = 0, k < n, k++, If[PrimeQ[a[k] + n - 1], cnt++]]; cnt); Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Sep 13 2013 *)

PROG

(PARI) {v=[1]; for(n=2, 250, w=vector(length(v)+1); s=0; for(i=1, length(v), w[i]=v[i]; if(isprime(v[i]+n-1), s++)); w[length(v)+1]=s; v=w); v} (Herrgesell)

(Haskell)

a114897 n = a114897_list !! (n-1)

a114897_list = 1 : f 1 [1] where

f x zs = z : f (x + 1) (z : zs) where

z = toInteger $ sum $ map (a010051 . (+ x)) zs

-- Reinhard Zumkeller, Jul 31 2012

CROSSREFS

Cf. A010051, A108839, A123541.

Sequence in context: A355531 A234809 A135591 * A360614 A210954 A195843

Adjacent sequences: A114894 A114895 A114896 * A114898 A114899 A114900

KEYWORD

nonn,nice

AUTHOR

Leroy Quet, Jan 05 2006

EXTENSIONS

More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Jan 16 2006

STATUS

approved