A233267 a(n) = A055881(A001110(n)); the largest m such that m! divides the n-th positive number which is both triangular and square.

1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 11, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1

Offset

1,2

Comments

The sequence seems to have a nice symmetric fractal structure. The new distinct values (records) occur at positions k = 1, 2, 4, 12, 48, 288, 2016, 4032, ... those values being 1, 3, 4, 7, 11, 12, 13, 14, ...

Furthermore, each prefix from 1 to 2*k-1 (centered on a new record) seems to be palindromic. 2*k-1 runs as: 1, 3, 7, 23, 95, 575, 4031, 8063, ...

On the other hand, if we list ALL the positions p where prefix 1..p is palindromic, we obtain a sequence: 1, 3, 7, 11, 23, 35, 47, 95, 143, 191, 239, 287, 575, 863, 1151, 1439, 1727, 2015, 4031, ...

Its first differences is again familiar: 2, 4, 4, 12, 12, 12, 48, 48, 48, 48, 48, 288, 288, 288, 288, 288, 288, 2016, ... which appear to consist of 1, 2, 3, 5, 6, ... copies of the first mentioned sequence from its term 2 onward.

None of these sequences (except maybe the last) are in the OEIS as of Dec 06 2013.

Note: A233269(n) = A055881(A001109(n)) seems to have the same overall structure, but some of the records are missing/different.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8063

Formula

a(n) = A055881(A001110(n)).

Prog

(Scheme)
(define (A233267 n) (A055881 (A001110 n)))

Crossrefs

Cf. A001110, A055881, A233269, A232096-A232098, A233285.

Sequence in context: A030757 A004592 A116992 * A090740 A094603 A165595

Adjacent sequences: A233264 A233265 A233266 * A233268 A233269 A233270

Keyword

nonn

Author

Antti Karttunen, Dec 06 2013

Status

approved