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.

A095061 Number of fibodd primes (A095081) in range [2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 2, 4, 4, 7, 18, 25, 54, 105, 178, 332, 637, 1165, 2194, 4161, 7770, 14800, 28100, 53525, 102394, 195938, 377301, 723938, 1391620, 2684760, 5178439, 10010119, 19362205, 37501838, 72702221, 141062816, 273985225, 532514962
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Formula

a(n) = A036378(n) - A095060(n) = A095066(n) + A095069(n).

Extensions

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

A095080 Fibeven primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with zero.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 23, 29, 31, 37, 41, 47, 71, 73, 79, 83, 89, 97, 107, 109, 113, 131, 139, 149, 151, 157, 167, 173, 181, 191, 193, 199, 223, 227, 233, 241, 251, 257, 269, 277, 283, 293, 311, 317, 337, 353, 359, 367, 379, 397, 401, 409, 419, 421
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Crossrefs

Intersection of A000040 and A022342. Union of A095082 and A095087. Cf. A095060, A095081.

Programs

  • Maple
    F:= combinat[fibonacci]:
    b:= proc(n) option remember; local j;
          if n=0 then 0
        else for j from 2 while F(j+1)<=n do od;
             b(n-F(j))+2^(j-2)
          fi
        end:
    a:= proc(n) option remember; local p;
          p:= `if`(n=1, 1, a(n-1));
          do p:= nextprime(p);
             if b(p)::even then break fi
          od; p
        end:
    seq(a(n), n=1..100);  # Alois P. Heinz, Mar 27 2016
  • Mathematica
    F = Fibonacci;
    b[n_] := b[n] = Module[{j},
         If[n == 0, 0, For[j = 2, F[j + 1] <= n, j++];
         b[n - F[j]] + 2^(j - 2)]];
    a[n_] := a[n] = Module[{p},
         p = If[n == 1, 1, a[n - 1]]; While[True,
         p = NextPrime[p]; If[ EvenQ[b[p]], Break[]]]; p];
    Array[a, 100] (* Jean-François Alcover, Jul 01 2021, after Alois P. Heinz *)
  • 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]=="0"
    print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 07 2017

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 1-3 of 3 results.