A095083 -id:A095083 - cp's OEIS frontend

A095063 Number of fibodious primes (A095083) in range [2^n,2^(n+1)].

1, 1, 1, 3, 4, 7, 14, 22, 41, 70, 133, 261, 433, 800, 1468, 2883, 5445, 10033, 19388, 36902, 70168, 134005, 256771, 493088, 947153, 1822376, 3514806, 6780667, 13103439, 25351723, 49085715, 95166843, 184656849, 358622060, 697126872

Offset: 1

Antti Karttunen, Jun 01 2004

Antti Karttunen and John Moyer, C-program for computing the initial terms of this sequence.
Index entries for sequences related to occurrences of various subsets of primes in range [2^n,2^(n+1)].

Cf. A036378, A095064, A095083.

a(n) = A036378(n) - A095064(n).

a(34)-a(35) from Amiram Eldar, Jun 13 2024

A095084 Fibevil primes, i.e., primes p whose Zeckendorf-expansion A014417(p) contains an even number of 1-fibits.

Original entry on oeis.org

7, 11, 23, 29, 37, 47, 53, 67, 83, 97, 101, 109, 127, 137, 139, 149, 157, 163, 193, 199, 223, 241, 263, 271, 277, 281, 283, 311, 317, 331, 337, 359, 373, 379, 389, 397, 409, 421, 439, 443, 461, 499, 503, 521, 547, 557, 563, 577, 593, 601, 607

Offset: 1

Antti Karttunen, Jun 01 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Antti Karttunen and John Moyer, C-program for computing the initial terms of this sequence.

Intersection of A000040 and A095096.

Cf. A014417, A095083, A095064.

Select[Flatten[Position[Mod[DigitCount[Select[Range[0, 6000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 0]] - 1, PrimeQ] (* Amiram Eldar, Feb 07 2023 *)

A095280 Lower Wythoff primes, i.e., primes in A000201.

Original entry on oeis.org

3, 11, 17, 19, 29, 37, 43, 53, 59, 61, 67, 71, 79, 97, 101, 103, 113, 127, 131, 137, 139, 163, 173, 179, 181, 197, 199, 211, 223, 229, 239, 241, 257, 263, 271, 281, 283, 307, 313, 317, 331, 347, 349, 359, 367, 373, 383, 389, 401, 409, 419, 433

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

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

For generalizations and conjectures, see A184774.

Robert Israel, Table of n, a(n) for n = 1..10000
Antti Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

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

R:= NULL: count:= 0:
for n from 1 while count < 100 do
  p:= floor(n*phi);
  if isprime(p) then R:= R,p; count:= count+1 fi
od:
R; # Robert Israel, Jan 17 2023

Mathematica
```
(See A184792.)
```

from math import isqrt
from itertools import count, islice
from sympy import isprime
def A095280_gen(): # generator of terms
    return filter(isprime,((n+isqrt(5*n**2)>>1) for n in count(1)))
A095280_list = list(islice(A095280_gen(),30)) # Chai Wah Wu, Aug 16 2022

A095281 Upper Wythoff primes, i.e., primes in A001950.

Original entry on oeis.org

2, 5, 7, 13, 23, 31, 41, 47, 73, 83, 89, 107, 109, 149, 151, 157, 167, 191, 193, 227, 233, 251, 269, 277, 293, 311, 337, 353, 379, 397, 421, 431, 439, 463, 479, 523, 541, 547, 557, 599, 607, 617, 641, 659, 683, 691, 701, 709, 719, 727, 733, 743

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

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

Antti Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Intersection of A000040 & A001950. Complement of A095280 in A000040. Cf. A095081, A095083, A095084, A095290.

from math import isqrt
from itertools import count, islice
from sympy import isprime
def A095281_gen(): # generator of terms
    return filter(isprime,((n+isqrt(5*n**2)>>1)+n for n in count(1)))
A095281_list = list(islice(A095281_gen(),30)) # Chai Wah Wu, Aug 16 2022

cp's OEIS Frontend

A095063 Number of fibodious primes (A095083) in range [2^n,2^(n+1)].

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A095084 Fibevil primes, i.e., primes p whose Zeckendorf-expansion A014417(p) contains an even number of 1-fibits.

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A095280 Lower Wythoff primes, i.e., primes in A000201.

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A095281 Upper Wythoff primes, i.e., primes in A001950.

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Python