A349958 -id:A349958 - cp's OEIS frontend

A374959 a(n) is the least k such that binomial(A349958(n), k) is a multiple of n.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 2, 4, 1, 3, 1, 2, 1, 2, 1, 3, 1, 1, 3, 2, 3, 2, 1, 4, 2, 3, 1, 3, 1, 3, 2, 8, 1, 5, 1, 2, 2, 6, 1, 4, 2, 3, 2, 2, 1, 3, 1, 2, 4, 1, 4, 4, 1, 2, 6, 4, 1, 5, 1, 2, 2, 4, 5, 2, 1, 3, 1, 2, 1, 3, 3, 4, 3

Offset: 1

Rémy Sigrist, Jul 25 2024

nonn

			For n = 12: the first multiple of 12 in Pascal's triangle appears in row 9; this row contains: 1, 9, 36, 84, 126, 126, 84, 36, 9, 1; the first multiple of 12 (36), appears at (0-based) index 2; so a(12) = 2.

Cf. A007318, A349958, A357327.

a(n) = { my (r = [1 % n], j); for (i = 0, oo, if (vecmin(r, &j)==0, return (j-1), r = (concat(0, r) + concat(r, 0)) % n;);); }

from math import comb
def A374959(n): return next(k for j in range(n+1) for k in range(j+1) if not (comb(j,k) % n)) # Chai Wah Wu, Jul 30 2024

A375082 a(n) = binomial(A349958(n),A374959(n))/n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 15, 1, 5, 1, 3, 1, 1, 1, 4, 1, 1, 5, 4, 1, 1, 1, 102, 2, 3, 1, 2, 1, 5, 1, 10659, 1, 91, 1, 6, 3, 33, 1, 325, 1, 1, 3, 7, 1, 2, 1, 8, 2, 1, 11, 5, 1, 2, 1463, 1, 1, 11, 1, 9, 4, 51, 6, 1, 1, 7, 1

Offset: 1

Pontus von Brömssen, Jul 29 2024

nonn

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A007318, A349958, A374959, A375083, A375084.

from math import comb
def A375082(n): return next(a for a, b in (divmod(comb(j,k),n) for j in range(n+1) for k in range(j+1)) if not b) # Chai Wah Wu, Jul 30 2024

A375083 Numbers k such that k is not the first multiple of k that appears in Pascal's triangle (read by rows), i.e., such that A375082(k) > 1.

Original entry on oeis.org

12, 14, 18, 22, 24, 26, 30, 33, 34, 38, 39, 40, 42, 44, 46, 48, 50, 51, 52, 54, 57, 58, 60, 62, 63, 65, 66, 68, 69, 72, 74, 75, 76, 77, 80, 82, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118

Offset: 1

Pontus von Brömssen, Jul 29 2024

nonn

Cf. A007318, A349958, A374959, A375082.

isok(k) = for (i=1, k-1, for (j=1, i, my(b=binomial(i, j)); if (((b % k) == 0), return(b!=k)););); \\ Michel Marcus, Jul 30 2024

from itertools import count, islice
from math import comb
def A375083_gen(): # generator of terms
    return filter(lambda n:next(c for c in (comb(j,k) for j in range(n+1) for k in range(j+1)) if not c%n)>n, count(1))
A375083_list = list(islice(A375083_gen(),20)) # Chai Wah Wu, Jul 30 2024

cp's OEIS Frontend

A374959 a(n) is the least k such that binomial(A349958(n), k) is a multiple of n.

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A375082 a(n) = binomial(A349958(n),A374959(n))/n.

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A375083 Numbers k such that k is not the first multiple of k that appears in Pascal's triangle (read by rows), i.e., such that A375082(k) > 1.

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Author

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Python