VOOZH about

URL: https://oeis.org/A379676

⇱ A379676 - OEIS

login
A379676
For n >= 0, a(n) is the least k >= 2 such that (n + 1)*(2*k + n) / 2 is a triangular number (A000217).
2
3, 7, 4, 15, 7, 5, 10, 31, 13, 6, 16, 12, 19, 10, 7, 63, 25, 11, 28, 22, 8, 15, 34, 21, 37, 16, 40, 9, 43, 20, 46, 127, 14, 21, 18, 10, 55, 25, 15, 19, 61, 26, 64, 45, 11, 30, 70, 44, 73, 31, 21, 55, 79, 35, 12, 70, 22, 36, 88, 18, 91, 40, 34, 255, 31, 13, 100, 19, 28, 24, 106, 92, 109, 46, 29, 78, 25, 14, 118, 91, 121, 51, 124, 63, 42, 55, 35, 39, 133, 43, 15
OFFSET
0,1
COMMENTS
Also for n >= 0, a(n) is the least k >= 2 such that the Sum_{i = 0..n} (k + i) is a triangular number (A000217). For k = 0, 1 the Sum is a triangular number for all n. The sequences A076114 and A076116 are for square sum and cube sum.
LINKS
FORMULA
For i >= 0, a(2^i - 1) = 2^(i + 2) - 1, max. values of a(n).
For i >= 0, a(i*(i + 3)/2) = i + 3, min. values of a(n).
For i >= 1, i is not from A083390, a(2*i) = (3*i + 1).
EXAMPLE
n = 4: the least k >= 2 such that (4 + 1)*(2*k + 4)/2 = 5*k + 10 is a triangular number is k = 7, thus a(4) = 7.
n = 5: the least k >= 2 such that (5 + 1)*(2*k + 5)/2 = 6*k + 15 is a triangular number is k = 5, thus a(5) = 5.
MATHEMATICA
a[n_] := Module[{k = 2}, While[! IntegerQ[Sqrt[4*(n + 1)*(2*k + n) + 1]], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Dec 30 2024 *)
PROG
(PARI) a(n) = my(k=2); while (!ispolygonal((n + 1)*(2*k + n)/2, 3), k++); k; \\ Michel Marcus, Dec 30 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Dec 29 2024
STATUS
approved