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A064722 a(1) = 0; for n >= 2, a(n) = n - (largest prime <= n). 17
0, 0, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
LINKS
FORMULA
a(n) = n - A007917(n).
a(n) = 0 iff n is 1 or a prime.
Computable also as a "commutator": pi(prime(m)) - prime(pi(m)) = A000720(A000040(m)]-A000040(A000720(m)). Labels position of composites between 2 consecutive primes. - Labos Elemer, Oct 19 2001
a(n) = a(n-1)*0^A010051(n) + 1 - A010051(n), a(1) = 0. - Reinhard Zumkeller, Mar 23 2006
a(n) = n mod A007917(n). - Michel Marcus, Aug 22 2014
a(n) = A049711(n+1) - 1 for n >= 2. - Pontus von Brömssen, Jul 31 2022
EXAMPLE
a(26) = 26 - 23 = 3, a(37) = 37 - 37 = 0.
MAPLE
0, seq(n - prevprime(n+1), n=2..100); # Robert Israel, Aug 25 2014
MATHEMATICA
Join[{0}, Table[n-NextPrime[n+1, -1], {n, 2, 110}]] (* Harvey P. Dale, Aug 23 2011 *)
PROG
(PARI) { for (n = 1, 1000, if (n>1, a=n - precprime(n), a=0); write("b064722.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 23 2009
CROSSREFS
Sequence in context: A318656 A215151 A305806 * A259748 A357728 A357681
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 13 2001
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)