The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A175527 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A175527

Digit sum of 13^n.
(history; published version)

#23 by M. F. Hasler at Sat May 20 14:48:17 EDT 2017

STATUS

editing

approved

#22 by M. F. Hasler at Sat May 20 14:42:34 EDT 2017

PROG

(PARI) a175527a(n)=sumdigits(13^n); \\ Michel Marcus, Nov 01 2013

STATUS

proposed

editing

Discussion

Sat May 20

14:48

M. F. Hasler: I put back a(n), because it's unlikely that this function will ever be of use somewhere. But * if* a function is useful, especially if it's useful not only for its own sake but also elsewhere, then it *must* have a name different from a(n). So why not give it the name of the sequence=function computes?? The function that computes sin(x) is usually named sin, the function that computes Gamma(z) is called Gamma, why not call Axxx the function that computes Axxx ??

#21 by Michel Marcus at Fri May 19 01:52:08 EDT 2017

STATUS

editing

proposed

Discussion

Fri May 19

02:49

Joerg Arndt: Why these silly edits in the Pari programs?

#20 by Michel Marcus at Fri May 19 01:51:07 EDT 2017

PROG

(PARI) A175527=aa175527(n)=sumdigits(13^n); \\ Michel Marcus, Nov 01 2013

STATUS

proposed

editing

Discussion

Fri May 19

01:52

Michel Marcus: rather like this ?

#19 by M. F. Hasler at Thu May 18 19:17:46 EDT 2017

STATUS

editing

proposed

Discussion

Fri May 19

00:28

Robert Israel: Since 13^3 == 1 (mod 9), a(n+3) == a(n) (mod 9).  If |a(n) - a(n+3)| is not very large, it's not too unlikely to be 0.

#18 by M. F. Hasler at Thu May 18 19:15:50 EDT 2017

COMMENTS

It is surprising that many values repeat twice (for 85, 91, 121, 133, 169 this happens at a(n) = a(n+3) (but 169 occurs later for a third time), for 193, 241, 292, ... the second occurrence comes later) while many other values never occur. Is there a simple explanation? - M. F. Hasler, May 18 2017

Discussion

Thu May 18

19:17

M. F. Hasler: (I noticed this for 325 & 358 which occur like 85, ... at n & n+3.)

#17 by M. F. Hasler at Thu May 18 18:46:53 EDT 2017

DATA

Discussion

Thu May 18

18:50

M. F. Hasler: Cutting the data section to 3 full lines.

#16 by M. F. Hasler at Thu May 18 18:46:06 EDT 2017

DATA

1, 4, 16, 19, 22, 25, 37, 40, 34, 46, 67, 52, 55, 58, 97, 73, 85, 88, 91, 85, 115, 91, 121, 106, 109, 121, 133, 118, 121, 133, 163, 184, 169, 181, 193, 169, 172, 175, 178, 199, 193, 214, 226, 238, 169, 190, 247, 241, 208, 247, 232, 253, 292, 241, 316, 292, 268, 271, 301, 286, 298, 337, 304, 325, 301, 358, 325, 328, 358, 343, 346, 331, 361, 382, 385, 397, 373, 403, 451, 400, 331, 397, 391, 457, 460, 454, 448, 442, 409, 457, 496, 508, 421, 514, 481, 493, 424, 472, 529, 532, 535

FORMULA

a(n) ~ 4.5*log_10(13)*n ~ 5.0127*n (conjectured). - M. F. Hasler, May 18 2017

PROG

(PARI) A175527=a(n) = sumdigits(13^n); \\ Michel Marcus, Nov 01 2013

STATUS

approved

editing

#15 by Bruno Berselli at Fri Nov 01 18:49:49 EDT 2013

STATUS

proposed

approved

#14 by Michel Marcus at Fri Nov 01 17:05:26 EDT 2013

STATUS

editing

proposed