OFFSET
0,13
COMMENTS
It is not known unconditionally whether there are infinitely many primitive weird numbers (PWN, A002975), although numerical data provides strong evidence: even the number of weird numbers of the form 2^k*p*q (A258882, A258333) seems to increase rapidly as k increases. Melfi has shown that Cramer's conjecture implies the infiniteness of PWN.
LINKS
Giuseppe Melfi, On the conditional infiniteness of primitive weird numbers, Journal of Number Theory, Volume 147, February 2015, Pages 508-514.
EXAMPLE
The first primitive weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10792, ..., so there is one between 2^6 and 2^7 = 128, one between 2^9 and 2^10 = 1024, one between 2^11 and 2^12 = 4096, three between 2^12 and 2^13, etc.
PROG
(PARI) a(n)=sum(n=2^n\2+1, 2^n, is_A002975(n*2))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
M. F. Hasler, Jul 30 2016
EXTENSIONS
a(39) from Amiram Eldar, Sep 02 2023
STATUS
approved