A305979 Filter sequence for a(Fermi-Dirac primes) = constant sequences.

1, 2, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 8, 2, 2, 9, 2, 10, 11, 12, 2, 13, 2, 14, 15, 16, 2, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 2, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 2, 40, 41, 42, 43, 44, 2, 45, 46, 47, 2, 48, 2, 49, 50, 51, 52, 53, 2, 54, 2, 55, 2, 56, 57, 58, 59, 60, 2, 61, 62, 63, 64, 65, 66, 67, 2, 68, 69, 70, 2

Offset: 1

Author

Antti Karttunen, Jul 02 2018

Keywords

• nonn

Comments

For all i, j:

a(i) = a(j) => A305976(i) = A305976(j).

a(i) = a(j) => A302791(i) = A302791(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A050376, A302777, A302778, A302791, A305975, A305976.

Programs

PARI

up_to = 100000;
partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
A209229(n) = (n && !bitand(n, n-1));
A302777(n) = A209229(isprimepower(n));
v302778 = partialsums(A302777,up_to);
A302778(n) = v302778[n];
A305979(n) = if(1==n,n,if(1==A302777(n),2,1+n-A302778(n)));

Formula

a(1) = 1; for n > 1, if A302777(n) is 1 [when n is in A050376], a(n) = 2, otherwise a(n) = 1 + n - A302778(n) = running count from 3 onward.