cp's OEIS Frontend

A259379 Numbers k of the form a - b + c, such that k^3 equals the decimal concatenation a//b//c and numbers k, b, and c have the same number of digits.

%I A259379 #63 May 10 2025 03:14:42
%S A259379 155,209,274,286,287,351,364,428,573,637,715,727,846,923,1095,1096,
%T A259379 2191,8905,18182,18183,81818,81819,326734,336634,663367,673267,
%U A259379 2727273,2727274,4545454,5454547,7272727,23529411,23529412,76470589
%N A259379 Numbers k of the form a - b + c, such that k^3 equals the decimal concatenation a//b//c and numbers k, b, and c have the same number of digits.
%C A259379 This sequence is infinite because it has several infinite subsequences. For example:
%C A259379   274, 326734, 332667334, 3..326..673..34 etc.;
%C A259379   364, 336634, 333666334, 3..36..63..34 etc.;
%C A259379   637, 663367, 666333667, 6..63..36..67 etc.;
%C A259379   727, 673267, 667332667, 6..673..326..67 etc.
%C A259379 Note that: 274 + 727 = 364 + 637 = 1001 and 326734 + 673267 = 336634 + 663367 = 1000001.
%C A259379 Many numbers come in pairs, like: (286, 287), (1095, 1096), (18182, 18183) but also bigger number (140017877, 140017878) and (859982123, 859982124).
%C A259379 140017877 + 859982124 = 140017878 + 859982123 = 1000000001.
%H A259379 Pieter Post, <a href="/A259379/b259379.txt">Table of n, a(n) for n = 1..189</a>
%e A259379 155^3 = 3723875 and 155 = 3 - 723 + 875.
%e A259379 715^3 = 365525875 and 715 = 365 - 525 + 875.
%o A259379 (Python)
%o A259379 def modb(n,m):
%o A259379     kk = 0
%o A259379     l = 1
%o A259379     while n > 0:
%o A259379         na = n % m
%o A259379         l += 1
%o A259379         kk += ((-1)**l) * na
%o A259379         n //= m
%o A259379     return kk
%o A259379 for n in range (100, 10**9):
%o A259379     ll = len(str(n))
%o A259379     if modb(n**3, 10**ll) == n:
%o A259379         print(n, end=', ') # corrected by _David Radcliffe_, May 09 2025
%o A259379 (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
%Y A259379 Cf. A056733, A101311, A118937, A118938, A228381, A257796, A258482.
%K A259379 nonn,base
%O A259379 1,1
%A A259379 _Pieter Post_, Jul 22 2015