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 1-3 of 3 results.

A095060 Number of fibeven primes (A095080) in range ]2^n,2^(n+1)].

Original entry on oeis.org

1, 2, 2, 3, 3, 9, 16, 25, 50, 83, 150, 286, 540, 975, 1865, 3515, 6588, 12620, 23835, 45486, 86811, 165822, 317770, 608517, 1170182, 2254124, 4342530, 8383468, 16197159, 31335332, 60680818, 117633364, 228260489, 443281943, 861677274
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Formula

a(n) = A036378(n) - A095061(n) = A095062(n) + A095067(n).

Extensions

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

A095081 Fibodd primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with one.

Original entry on oeis.org

17, 19, 43, 53, 59, 61, 67, 101, 103, 127, 137, 163, 179, 197, 211, 229, 239, 263, 271, 281, 307, 313, 331, 347, 349, 373, 383, 389, 433, 449, 457, 467, 491, 499, 509, 569, 577, 593, 601, 619, 643, 653, 661, 677, 739, 773, 787, 797, 821, 823
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Intersection of A000040 and A003622. Union of A095086 and A095089. Cf. A095061, A095080.

Programs

  • Mathematica
    r = Map[Fibonacci, Range[2, 12]]; Select[Prime@ Range@ 144, Last@ Flatten@ Map[Position[r, #] &, Abs@ Differences@ NestWhileList[Function[k, k - SelectFirst[Reverse@ r, # < k &]], # + 1, # > 1 &]] == 1 &] (* Michael De Vlieger, Mar 27 2016, Version 10 *)
  • PARI
    genit(maxx)={for(n=1,maxx,q=(n-1)+(n+sqrtint(5*n^2))\2; if(isprime(q), print1(q,",")));} \\ Bill McEachen, Mar 26 2016
    
  • 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))[-1]=="1"
    print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 07 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
Showing 1-3 of 3 results.