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.

A275810 First differences of A275809.

Original entry on oeis.org

5, 9, 5, 3, 32, 5, 15, 10, 5, 4, 4, 3, 11, 3, 5, 145, 5, 9, 5, 3, 80, 5, 37, 5, 9, 5, 3, 10, 23, 3, 16, 10, 5, 4, 35, 16, 5, 9, 5, 3, 5, 10, 3, 4, 5, 3, 11, 3, 5, 32, 3, 17, 10, 3, 4, 4, 5, 9, 5, 3, 842, 5, 9, 5, 3, 32, 5, 15, 10, 5, 4, 4, 3, 11, 3, 5, 505, 5, 9, 5, 3, 194, 5, 9, 5, 3, 32, 5, 15, 10, 5, 4, 4, 3, 11, 3, 5, 31, 5, 111, 10, 5, 4, 100
Offset: 1

Views

Author

Antti Karttunen, Aug 09 2016

Keywords

Crossrefs

Cf. A275809.

Programs

Formula

a(n) = A275809(n) - A275809(n-1).

A275805 Indices of nonsquarefree terms in A275734; numbers with at least one digit slope (in their factorial base representation) with multiple nonzero digits. (See comments for the exact definition).

Original entry on oeis.org

5, 11, 14, 15, 17, 19, 21, 22, 23, 29, 35, 38, 39, 41, 43, 45, 46, 47, 53, 54, 55, 56, 57, 58, 59, 62, 63, 65, 67, 69, 70, 71, 74, 75, 77, 80, 81, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 125, 131, 134, 135, 137, 139, 141, 142, 143, 149, 155
Offset: 1

Views

Author

Antti Karttunen, Aug 10 2016

Keywords

Comments

Numbers n for which A008683(A275734(n)) = 0.
Numbers n for which A275811(n) > 1.
Numbers n in whose factorial base representation (A007623) there exists at least one pair of digit positions i_1 and i_2 with nonzero digits d_1 and d_2 such that (i_1 - d_1) = (i_2 - d_2).

Examples

			For n=5, "21" in factorial base (A007623), the pair 2 (in position 2) and 1 (in position 1) satisfies the condition, as (2-2) = (1-1), thus 5 is included.
For n=55, "2101" in factorial base, the pair 2 (in position 4) and 1 (in position 3) satisfies the condition, as (4-2) = (3-1), thus 55 is included.
For n=67, "2301" in factorial base, the pair 3 (in position 3) and 1 (in position 1) satisfies the condition, as (3-3) = (1-1), thus 67 is included in the sequence.
		

Crossrefs

Complement: A275804.
Cf. A275809 (a subsequence apart from its initial 0-term).
Subsequence of A115945.

Programs

  • Python
    from operator import mul
    from sympy import prime, factorial as f, mobius
    from functools import reduce
    def a007623(n, p=2): return n if n

    0 else '0' for i in x)[::-1] return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))]) def a(n): return 1 if n==0 else a275732(n)*a(a257684(n)) print([n for n in range(201) if mobius(a(n))==0]) # Indranil Ghosh, Jun 19 2017

A275808 a(0) = 0, for n >= 1, a(n) = A275736(n) XOR a(A257684(n)), where XOR is given by A003987.

Original entry on oeis.org

0, 1, 2, 3, 1, 0, 4, 5, 6, 7, 5, 4, 2, 3, 0, 1, 3, 2, 1, 0, 3, 2, 0, 1, 8, 9, 10, 11, 9, 8, 12, 13, 14, 15, 13, 12, 10, 11, 8, 9, 11, 10, 9, 8, 11, 10, 8, 9, 4, 5, 6, 7, 5, 4, 0, 1, 2, 3, 1, 0, 6, 7, 4, 5, 7, 6, 5, 4, 7, 6, 4, 5, 2, 3, 0, 1, 3, 2, 6, 7, 4, 5, 7, 6, 0, 1, 2, 3, 1, 0, 3, 2, 1, 0, 2, 3, 1, 0, 3, 2, 0
Offset: 0

Views

Author

Antti Karttunen, Aug 09 2016

Keywords

Crossrefs

Cf. A275809 (positions of zeros), A275810 (and their first differences).
Cf. also A275728.

Formula

a(0) = 0, for n >= 1, a(n) = A275736(n) XOR a(A257684(n)), where 2-argument function XOR is given by A003987.
a(n) = A248663(A275734(n)).

A275813 Positions of odd terms in A060131; indices of permutations of an odd order in tables A060117 & A060118.

Original entry on oeis.org

0, 3, 5, 8, 10, 13, 14, 19, 22, 30, 33, 35, 36, 39, 41, 42, 45, 47, 50, 52, 54, 57, 59, 63, 65, 69, 71, 73, 74, 81, 83, 84, 87, 89, 93, 95, 97, 100, 105, 107, 111, 113, 114, 117, 119, 144, 147, 149, 152, 154, 157, 158, 163, 166, 168, 171, 173, 176, 178, 181, 182, 187, 190, 192, 195, 197, 200, 202, 205, 206, 211, 214, 216, 219, 221
Offset: 0

Views

Author

Antti Karttunen, Aug 10 2016

Keywords

Comments

Indexing starts with zero, because a(0) = 0 (indicating an identity permutation) is a special case in this sequence.

Crossrefs

Complement: A275814.
Cf. A275809 (a subsequence).
Showing 1-4 of 4 results.