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.

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A253789 Fixed points of f(n) = A252753(n-1).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 128, 160, 192, 256, 320, 384, 481, 512, 640, 768, 962, 1024, 1280, 1536, 1924, 2048, 2560, 3072, 3848, 4096, 5120, 6144, 7696, 8192, 10240, 12288, 15392, 16384, 20480, 24576
Offset: 1

Views

Author

Antti Karttunen, Jan 13 2015

Keywords

Crossrefs

Cf. A252753.
Also fixed points of f(n) = A252754(n)+1.
Differs from a subsequence A029747 for the first time at n=25, where a(25) = 481, while A029747 contains no odd terms after 1, 3 and 5.
No other odd numbers can occur than those listed at A253790.

A286254 Compound filter: a(n) = P(A001511(n), A055396(1+n)), where P(n,k) is sequence A000027 used as a pairing function.

Original entry on oeis.org

1, 5, 1, 13, 1, 12, 1, 14, 1, 17, 1, 31, 1, 5, 1, 60, 1, 38, 1, 9, 1, 47, 1, 19, 1, 5, 1, 69, 1, 68, 1, 27, 1, 8, 1, 94, 1, 5, 1, 124, 1, 107, 1, 9, 1, 122, 1, 33, 1, 5, 1, 156, 1, 8, 1, 14, 1, 155, 1, 193, 1, 5, 1, 43, 1, 192, 1, 9, 1, 212, 1, 280, 1, 5, 1, 18, 1, 255, 1, 20, 1, 278, 1, 13, 1, 5, 1, 355, 1, 12, 1, 9, 1, 8, 1, 441, 1, 5, 1, 381, 1, 380, 1, 14
Offset: 1

Views

Author

Antti Karttunen, May 07 2017

Keywords

Links

Crossrefs

Cf. A000027, A001511, A055396, A253790, A286161, A286251, A286252, A286253.

Programs

  • PARI
    A001511(n) = (1+valuation(n,2));
A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015
A286254(n) = (2 + ((A001511(n)+A055396(1+n))^2) - A001511(n) - 3*A055396(1+n))/2;
for(n=1, 10000, write("b286254.txt", n, " ", A286254(n)));
  • Python
    from sympy import primepi, isprime, primefactors
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a049084(n): return primepi(n)*(1*isprime(n))
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a001511(n), a055396(n + 1)) # Indranil Ghosh, May 07 2017
  • Scheme
    (define (A286254 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A055396 (+ 1 n))) 2) (- (A001511 n)) (- (* 3 (A055396 (+ 1 n)))) 2)))

Formula

a(n) = (1/2)*(2 + ((A001511(n)+A055396(1+n))^2) - A001511(n) - 3*A055396(1+n)).
Showing 1-2 of 2 results.

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