login
A072491
Define f(1) = 0. For n>=2, let f(n) = n - p where p is the largest prime <= n. a(n) = number of iterations of f to reach 0, starting from n.
4
0, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 2, 3, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2
OFFSET
0,5
COMMENTS
a(p)=1, a(p+1)=2 and a(p+4)=3 if p is an odd prime but p+2 and p+4 are composite.
Number of noncomposites (A008578) needed to sum to n using the greedy algorithm. - Antti Karttunen, Aug 09 2015
REFERENCES
S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp. 159-167.
LINKS
FORMULA
On Cramér's conjecture, a(n) = O(log* n). - Charles R Greathouse IV, Feb 04 2013
EXAMPLE
a(27)=3 as f(27)=27-23=4, f(4)=4-3=1 and f(1)=0.
MATHEMATICA
f[1]=0; f[n_] := n-Prime[PrimePi[n]]; a[n_] := Module[{k, x}, For[k=0; x=n, x>0, k++; x=f[x], Null]; k]
PROG
(PARI) a(n)=if(n<4, n>0, 1+a(n-precprime(n))) \\ Charles R Greathouse IV, Feb 04 2013
CROSSREFS
Cf. A008578, A072492. A066352(n) is the smallest k such that a(k)=n.
Not the same as A051034: a(122) = 3, but A051034(122) = 2.
Sequence in context: A072410 A342824 A344713 * A051034 A024935 A082477
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Jul 14 2002
EXTENSIONS
Edited by Dean Hickerson, Nov 26 2002
a(0) = 0 prepended by Antti Karttunen, Aug 09 2015
STATUS
approved