A095280 - OEIS

%I #18 Jan 17 2023 15:34:37

%S 3,11,17,19,29,37,43,53,59,61,67,71,79,97,101,103,113,127,131,137,139,

%T 163,173,179,181,197,199,211,223,229,239,241,257,263,271,281,283,307,

%U 313,317,331,347,349,359,367,373,383,389,401,409,419,433

%N Lower Wythoff primes, i.e., primes in A000201.

%C Contains all primes p whose Zeckendorf-expansion A014417(p) ends with an even number of 0's.

%C For generalizations and conjectures, see A184774.

%H Robert Israel, <a href="/A095280/b095280.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%p R:= NULL: count:= 0:

%p for n from 1 while count < 100 do

%p   p:= floor(n*phi);

%p   if isprime(p) then R:= R,p; count:= count+1 fi

%p od:

%p R; # _Robert Israel_, Jan 17 2023

%t (See A184792.)

%o (Python)

%o from math import isqrt

%o from itertools import count, islice

%o from sympy import isprime

%o def A095280_gen(): # generator of terms

%o     return filter(isprime,((n+isqrt(5*n**2)>>1) for n in count(1)))

%o A095280_list = list(islice(A095280_gen(),30)) # _Chai Wah Wu_, Aug 16 2022

%Y Intersection of A000040 & A000201. Complement of A095281 in A000040. Cf. A095080, A095083, A095084, A095290, A184792, A184793, A184794, A184796.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 04 2004