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A259379 Numbers n of the form a - b + c, such that n^3 equals the decimal concatenation a//b//c and numbers n, b, and c have the same number of digits. 2
155, 209, 274, 286, 287, 351, 364, 428, 573, 637, 715, 727, 846, 923, 1095, 1096, 2191, 8905, 18182, 18183, 81818, 81819, 326734, 336634, 663367, 673267, 2727273, 2727274, 4545454, 5454547, 7272727, 23529411, 23529412, 76470589 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is infinite because it has several infinite subsequences. For example:

274, 326734, 332667334, 3..326..673..34 etc.;

364, 336634, 333666334, 3..36..63..34 etc.;

637, 663367, 666333667, 6..63..36..67 etc.;

727, 673267, 667332667, 6..673..326..67 etc.

Note that: 274 + 727 = 364 + 637 = 1001 and 326734 + 673267 = 336634 + 663367 = 1000001.

Many numbers come in pairs, like: (286, 287), (1095, 1096), (18182, 18183) but also bigger number (140017877, 140017878) and (859982123, 859982124).

140017877 + 859982124 = 140017878 + 859982123 = 1000000001.

LINKS

Pieter Post, Table of n, a(n) for n = 1..189

EXAMPLE

155^3 = 3723875 and 155 = 3 - 723 + 875.

715^3 = 365525875 and 715 = 365 - 525 + 875.

PROG

(Python)

def modb(n, m):

...kk = 0

....l=1

....while n > 0:

........na=int(n%m)

........l=l+1

........kk= kk+((-1)**l)*na

........n =int(n//m)

....return kk

for n in range (100, 10**9):

....ll= len(str(n))

....if modb(n**3, 10**ll)==n:

.........print (n)

(PARI) isok(n)=nb = #digits(n, 10); if (a = n^3 \ 10^(2*nb), c = n^3 % 10^nb; b = (n^3 - a*10^(2*nb))\10^nb; n^3 == (a-b+c)^3; ); \\ Michel Marcus, Aug 05 2015

CROSSREFS

Cf. A056733, A101311, A118937, A118938, A228381, A257796, A258482.

Sequence in context: A248657 A159258 A214472 * A122475 A252805 A089256

Adjacent sequences:  A259376 A259377 A259378 * A259380 A259381 A259382

KEYWORD

nonn,base

AUTHOR

Pieter Post, Jul 22 2015

STATUS

approved

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Last modified March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)