A078772 a(n) = phi(n-p) where p is largest prime < n, a(1) = a(2) = 1 by convention.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 4, 2, 1, 1, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 4, 2, 1, 1, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 4, 2, 6, 4, 1, 1, 2

Offset: 1

Author

Jon Perry, Jan 09 2003

Keywords

• nonn

Comments

This sequence is a block of concatenations of vectors of lengths of prime gaps with elements phi(i) for i = 1 to that prime gap. Those vectors are (1), (1, 1), (1, 1, 2, 2), (1, 1, 2, 2, 4, 2), ... - David A. Corneth, Oct 20 2017

Examples

			a(10) = phi(10-7) = phi(3) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000010, A001223, A049711.

Programs

PARI

for (n=1,100, print1(eulerphi(n-precprime(n-1))","))

PARI

first(n) = {n = nextprime(n); my(res = vector(n), phimap = Map(), q = 2, v); res[1] = res[2] = 1; forprime(p=3, n, if(!mapisdefined(phimap, p - q), mapput(phimap, p - q, vector(p - q, i, eulerphi(i)))); v = mapget(phimap, p-q); for(i = q + 1, p, res[i] = v[i - q]); q = p); res} \\ David A. Corneth, Oct 20 2017

Formula

For n >= 3, a(n) = A000010(A049711(n)). - Antti Karttunen, Oct 20 2017

Extensions

Description clarified by Antti Karttunen, Oct 20 2017