The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A305979 Filter sequence for a(Fermi-Dirac primes) = constant sequences. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For all i, j:
a(i) = a(j) => A305976(i) = A305976(j).
a(i) = a(j) => A302791(i) = A302791(j).
LINKS
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.
PROG
(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)));
CROSSREFS
Sequence in context: A293444 A302791 A334868 * A366805 A293223 A361514
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 02 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 18:37 EDT 2024. Contains 372664 sequences. (Running on oeis4.)