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 1-4 of 4 results.

A276339 a(n) = A255411(n) - A276340(n).

Original entry on oeis.org

0, 0, 4, 4, 0, 0, 22, 22, 24, 24, 22, 22, 18, 18, 22, 22, 18, 18, 0, 0, 4, 4, 0, 0, 118, 118, 120, 120, 118, 118, 138, 138, 142, 142, 138, 138, 120, 120, 124, 124, 120, 120, 118, 118, 120, 120, 118, 118, 114, 114, 118, 118, 114, 114, 120, 120, 124, 124, 120, 120, 118, 118, 120, 120, 118, 118, 114, 114, 118, 118, 114, 114, 96
Offset: 0

Views

Author

Antti Karttunen, Sep 01 2016

Keywords

Crossrefs

Cf. A276091 (seems to give the indices of zeros, checked empirically for the first 512 zeros).

Programs

Formula

a(n) = A255411(n) - A276340(n).

A276341 Complement of A276340.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101
Offset: 1

Views

Author

Antti Karttunen, Sep 01 2016

Keywords

Crossrefs

Cf. A276340 (complement).
Cf. A276326.

A276091 Numbers obtained by reinterpreting base-2 representation of n in A001563-base (A276326): a(n) = Sum_{k>=0} A030308(n,k)*A001563(k+1).

Original entry on oeis.org

0, 1, 4, 5, 18, 19, 22, 23, 96, 97, 100, 101, 114, 115, 118, 119, 600, 601, 604, 605, 618, 619, 622, 623, 696, 697, 700, 701, 714, 715, 718, 719, 4320, 4321, 4324, 4325, 4338, 4339, 4342, 4343, 4416, 4417, 4420, 4421, 4434, 4435, 4438, 4439, 4920, 4921, 4924, 4925, 4938, 4939, 4942, 4943, 5016, 5017, 5020, 5021, 5034, 5035, 5038, 5039, 35280, 35281
Offset: 0

Views

Author

Antti Karttunen, Aug 19 2016

Keywords

Comments

Numbers that are sums of distinct terms of A001563.
A number is included if and only if all the nonzero digits in its factorial base representation (A007623) are maximal allowed in those digit positions, thus this sequence gives all numbers n for which A060130(n) = A260736(n).
Numbers n for which A276328(n) = A276337(n), thus from 1 onward the positions of ones in A276336.
Conjectured also to give all numbers n for which A255411(n) = A276340(n) (thus zeros of A276339).

Crossrefs

Programs

  • Mathematica
    Table[Total[Times @@@ Transpose@ {Map[# #! &, Range@ Length@ #], Reverse@ #}] &@ IntegerDigits[n, 2], {n, 64}] (* Michael De Vlieger, Aug 31 2016 *)
  • Python
    from sympy import factorial as f
    def a007623(n, p=2): return n if n

    0 else '0' for i in x)[::-1] return 0 if n==0 else sum(int(y[i])*f(i + 1) for i in range(len(y))) def a(n): return 0 if n==0 else a255411(a(n//2)) if n%2==0 else 1 + a255411(a((n - 1)//2)) print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 20 2017

  • Scheme
    ;; This is a standalone program:
    (define (A276091 n) (let loop ((n n) (s 0) (f 1) (i 2)) (cond ((zero? n) s) ((even? n) (loop (/ n 2) s (* i f) (+ 1 i))) (else (loop (/ (- n 1) 2) (+ s (* (- i 1) f)) (* i f) (+ 1 i))))))
    ;; This implements one of the given recurrences:
    (definec (A276091 n) (cond ((zero? n) n) ((even? n) (A255411 (A276091 (/ n 2)))) (else (+ 1 (A255411 (A276091 (/ (- n 1) 2)))))))
    ;; Alternatively, we can use A276340 in place of A255411:
    (definec (A276091 n) (cond ((zero? n) n) ((even? n) (A276340 (A276091 (/ n 2)))) (else (+ 1 (A276340 (A276091 (/ (- n 1) 2)))))))
    

Formula

a(0) = 0, a(2n) = A255411(a(n)), a(2n+1) = 1+A255411(a(n)).
a(0) = 0, a(2n) = A276340(a(n)), a(2n+1) = 1+A276340(a(n)).
Other identities. For all n >= 0:
a(n) = A225901(A059590(n)).
a(n) = A276090(A275959(n)).
A276328(a(n)) = A276337(a(n)) = A000120(n).

Extensions

Name changed (to emphasize the functional nature of the sequence) with the original definition moved to the comments by Antti Karttunen, Sep 01 2016

A276338 a(n) = A276333(n) * A001563(1+A258198(n)).

Original entry on oeis.org

0, 4, 8, 12, 18, 18, 18, 18, 36, 36, 36, 36, 54, 54, 54, 54, 72, 72, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 384
Offset: 0

Views

Author

Antti Karttunen, Sep 01 2016

Keywords

Comments

a(n) is obtained by first replacing with zeros all other digits except the leftmost (the most significant) in the greedy A001563-base representation of n (A276326), then appending an extra zero to the right, then converting back to decimal.
An auxiliary function for computing A276340.

Crossrefs

Programs

Formula

a(n) = A276333(n) * A001563(1+A258198(n)).
Other identities. For all n >= 0:
a(n) = A276340(A276334(n)).
Showing 1-4 of 4 results.