A396382 - OEIS

A396382

A(n,k) read by falling antidiagonals, where A(n,k) is the least positive integer m such that n divides m and k divides m+1; if no such m exists, then A(n,k)=0.

1, 1, 2, 2, 0, 3, 3, 2, 3, 4, 4, 0, 0, 0, 5, 5, 4, 3, 8, 5, 6, 6, 0, 9, 0, 5, 0, 7, 7, 6, 0, 4, 15, 0, 7, 8, 8, 0, 6, 0, 0, 0, 14, 0, 9, 9, 8, 15, 20, 5, 24, 7, 8, 9, 10, 10, 0, 0, 0, 20, 0, 14, 0, 0, 0, 11, 11, 10, 9, 8, 15, 6, 35, 24, 27, 20, 11, 12, 12, 0, 21, 0, 35, 0, 0, 0, 9, 0, 11, 0, 13

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

OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals)

FORMULA

From Robert Israel, Jun 24 2026: (Start)

A(n,k) = 0 if GCD(n,k) > 1.

A(n,1) = n.

Otherwise A(n,k) = n * (-n^(-1) mod k). (End)

EXAMPLE

Table begins:

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ...

2, 0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, ...

3, 3, 0, 3, 9, 0, 6, 15, 0, 9, 21, 0, 12, 27, 0, ...

4, 0, 8, 0, 4, 0, 20, 0, 8, 0, 32, 0, 12, 0, 44, ...

5, 5, 5, 15, 0, 5, 20, 15, 35, 0, 10, 35, 25, 55, 0, ...

6, 0, 0, 0, 24, 0, 6, 0, 0, 0, 54, 0, 12, 0, 0, ...

7, 7, 14, 7, 14, 35, 0, 7, 35, 49, 21, 35, 77, 0, 14, ...

8, 0, 8, 0, 24, 0, 48, 0, 8, 0, 32, 0, 64, 0, 104, ...

9, 9, 0, 27, 9, 0, 27, 63, 0, 9, 54, 0, 90, 27, 0, ...

10, 0, 20, 0, 0, 0, 20, 0, 80, 0, 10, 0, 90, 0, 0, ...

MAPLE

f:= proc(n, k)

if igcd(n, k)<>1 then 0

elif k = 1 then n

else

n * (-n^(-1) mod k)

end proc:

Matrix(10, 10, f); # Robert Israel, Jun 24 2026

CROSSREFS

Cf. A127465.

Sequence in context: A071426 A288530 A295675 * A135356 A259016 A379225

Adjacent sequences: A396379 A396380 A396381 * A396383 A396384 A396385

KEYWORD

nonn,tabl

AUTHOR

Ali Sada, Jun 23 2026

STATUS

approved