A336346 -id:A336346

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A338118

a(n) = Product_{k = n+1-A336346(n)..n} A336346(n).

+20
2

1, 2, 4, 12, 6, 18, 72, 8, 24, 96, 36, 144, 192, 48, 720, 10, 30, 120, 600, 60, 45, 27, 108, 540, 240, 320, 1600, 2000, 75, 300, 1500, 9000, 90, 54, 216, 1080, 900, 400, 7200, 480, 384, 1920, 2400, 14400, 3000, 3750, 22500, 4500, 27000, 189000, 14, 42, 168

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

All terms are composite except a(1) = 1 and a(2) = 2.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 25000 terms (where the hue is function of A336346(n))

Rémy Sigrist, PARI program for A338118

EXAMPLE

A336346(4) = 3, so a(4) = A336346(2) * A336346(3) * A336346(4) = 2 * 2 * 3 = 12.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A336346.

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Oct 21 2020

STATUS

approved

A338283

Lexicographically earliest sequence of positive integers such that for any distinct m and n, Sum_{k = m+1-a(m)..m} a(k) <> Sum_{k = n+1-a(n)..n} a(k).

+10
4

1, 2, 2, 3, 2, 3, 4, 2, 3, 4, 3, 4, 4, 3, 5, 4, 5, 4, 4, 5, 5, 6, 4, 5, 6, 5, 6, 5, 6, 6, 5, 7, 6, 6, 7, 6, 5, 7, 8, 4, 8, 6, 6, 7, 8, 6, 7, 7, 8, 6, 7, 8, 7, 8, 8, 8, 6, 9, 7, 8, 8, 9, 8, 7, 8, 9, 8, 9, 8, 9, 10, 8, 9, 9, 8, 10, 9, 9, 10, 8, 10, 9, 10, 9, 9

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

In other words, for any n > 0, the sum of the a(n) terms up to and including a(n) is always unique.

This sequence is unbounded.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A338283

EXAMPLE

The first terms, alongside the corresponding sums, are:

n a(n) a(n+1-a(n))+...+a(n)

-- ---- --------------------

1 1 1

2 2 3

3 2 4

4 3 7

5 2 5

6 3 8

7 4 12

8 2 6

9 3 9

10 4 13

PROG

(PARI) See Links section.

CROSSREFS

See A336346 and A338292 for similar sequences.

Cf. A338285 (corresponding sums).