A375573 Numbers occurring at least three times in Bernoulli's triangle A008949.

1, 16, 64, 232, 256, 466, 562, 1024, 1486, 2048, 4096, 15226, 16384, 44552, 65536, 262144, 1048576, 4194304, 16777216, 67108864, 268435456, 1073741824, 4294967296, 17179869184, 68719476736, 274877906944, 1099511627776, 4398046511104, 17592186044416, 70368744177664

Offset: 1

Author

Pontus von Brömssen, Aug 19 2024

Keywords

• nonn

Comments

Equivalently, 1 together with numbers occurring at least three times in columns k >= 1 of Bernoulli's triangle.

Equivalently, 1 together with numbers occurring at least twice in columns k >= 2 of Bernoulli's triangle.

4^j is a term if j >= 0 and j != 1, because 4^j = A008949(2*j,2*j) = A008949(2*j+1,j) = A008949(4^j-1,1) for j >= 2 and A008949(i,0) = 1 for all i. Are 232, 466, 562, 1486, 2048, 15226, 44552 the only terms not of this form? There are no more such terms below 2^70.

Are 1 and 4096 = A008949(12,12) = A008949(13,6) = A008949(90,2) = A008949(4095,1) the only numbers that occur at least 4 times? There are no more such numbers below 2^70.

Crossrefs

Cf. A003015, A008949, A374796, A375570, A375572.