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A233267 a(n) = A055881(A001110(n)); the largest m such that m! divides the n-th positive number which is both triangular and square. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 21:23 EDT 2019. Contains 323410 sequences. (Running on oeis4.)