cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A095064 Number of fibevil primes (A095084) in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 1, 1, 2, 3, 6, 9, 21, 34, 67, 122, 203, 439, 812, 1562, 2826, 5304, 10357, 19247, 36684, 70168, 134211, 256937, 492730, 946967, 1823368, 3512484, 6781240, 13103839, 25345814, 49096941, 95168742, 184666456, 358645108, 697065364
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Formula

a(n) = A036378(n) - A095063(n).

Extensions

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

A095096 Fibevil numbers: those numbers k for which the parity of 1-fibits in Zeckendorf expansion A014417(k) is even, i.e., for which A095076(k) = 0.

Original entry on oeis.org

0, 4, 6, 7, 9, 10, 11, 14, 15, 16, 18, 22, 23, 24, 26, 29, 33, 35, 36, 37, 39, 42, 46, 47, 51, 53, 54, 56, 57, 58, 60, 63, 67, 68, 72, 74, 75, 76, 80, 82, 83, 85, 86, 87, 90, 91, 92, 94, 97, 101, 102, 106, 108, 109, 110, 114, 116, 117, 119, 120, 121, 123, 127, 129
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Characteristic function: A095111.
Complement of A020899.
Cf. A001969 (evil numbers), A014417, A095076, A095084 (fibevil primes).

Programs

  • Maple
    A095096 := proc(n)
        option remember;
        local a;
        if n =1 then
            0;
        else
            for a from procname(n-1)+1 do
                if A095076(a) = 0 then
                    return a;
                end if;
            end do:
        end if;
    end proc:
    seq(A095096(n),n=1..60) ; # R. J. Mathar, Sep 22 2020
  • Mathematica
    Flatten @ Position[Mod[DigitCount[Select[Range[0, 1000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 0] - 1  (* Amiram Eldar, Feb 05 2023 *)

Extensions

Changed offset to 1. - N. J. A. Sloane, Sep 12 2020

A095083 Fibodious primes, i.e., primes p whose Zeckendorf-expansion A014417(p) contains an odd number of 1-fibits.

Original entry on oeis.org

2, 3, 5, 13, 17, 19, 31, 41, 43, 59, 61, 71, 73, 79, 89, 103, 107, 113, 131, 151, 167, 173, 179, 181, 191, 197, 211, 227, 229, 233, 239, 251, 257, 269, 293, 307, 313, 347, 349, 353, 367, 383, 401, 419, 431, 433, 449, 457, 463, 467, 479, 487, 491
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Intersection of A000040 and A020899.

Programs

  • Mathematica
    Select[Flatten[Position[Mod[DigitCount[Select[Range[0, 5000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1]] - 1, PrimeQ] (* Amiram Eldar, Feb 07 2023 *)
  • Python
    from sympy import fibonacci, primerange
    def a(n):
        k=0
        x=0
        while n>0:
            k=0
            while fibonacci(k)<=n: k+=1
            x+=10**(k - 3)
            n-=fibonacci(k - 1)
        return x
    def ok(n): return str(a(n)).count("1")%2
    print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 08 2017

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

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

Contains all primes p whose Zeckendorf-expansion A014417(p) ends with an even number of 0's.
For generalizations and conjectures, see A184774.

Crossrefs

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

Programs

  • Maple
    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.)
  • Python
    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

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

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

Crossrefs

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

Programs

  • Python
    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
Showing 1-5 of 5 results.