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.

A384386 Number of integers with a shortest addition-multiplication-composition chain of length n, starting with 1 and x, i.e., number of integers k with A384384(k) = n.

Original entry on oeis.org

1, 1, 2, 5, 16, 82, 907
Offset: 0

Views

Author

Pontus von Brömssen, Jun 01 2025

Keywords

Comments

See A384383 and A384384 for details.

Crossrefs

Cf. A383002 (addition and multiplication), A384383, A384384, A384385, A384485 (addition and composition).

A384385 Smallest number with shortest addition-multiplication-composition chain of length n, starting with 1 and x, i.e., smallest k such that A384384(k) = n.

Original entry on oeis.org

1, 2, 3, 5, 7, 13, 23, 95
Offset: 0

Views

Author

Pontus von Brömssen, Jun 01 2025

Keywords

Comments

See A384383 and A384384 for details.

Crossrefs

Cf. A383001 (addition and multiplication), A384383, A384384, A384386, A384484 (addition and composition).

A384483 Length of shortest addition-composition chain for n, starting with 1 and x.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 5, 5, 6, 5, 5, 5, 5, 6, 6, 6, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 5, 6, 6, 6, 6, 6, 7
Offset: 1

Views

Author

Pontus von Brömssen, Jun 02 2025

Keywords

Comments

See A384480 for the definition of addition-composition chains. The number n is identified with the constant function f(x) = n.

Examples

			The smallest n for which a(n) < A003313(n) is n = 21. The length of a shortest addition chain for 21 is A003313(21) = 6, but there are addition-composition chains of length 5, for example (1, x,) x+1, 2*x+2, 3*x+3, 6, 21. 6 and 21 are the compositions of 3*x+3 with 1 and 6, respectively.

Crossrefs

Row 0 of A384480 for columns k >= 1.
Cf. A003313 (addition only), A230697 (addition and multiplication), A384384 (addition, multiplication, and composition), A384484, A384485.

Formula

a(n) <= A003313(n).
a(n) <= a(n-1) + 1.
Showing 1-3 of 3 results.

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