The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A352759 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A352759

Centered cube numbers that are the difference of two positive cubes; a(n) = 27*t^3*(27*t^6 + 1)/4 with t = 2*n-1.
(history; published version)

#39 by N. J. A. Sloane at Sat Jul 16 00:55:21 EDT 2022

STATUS

proposed

approved

#38 by Vladimir Pletser at Fri Jul 15 23:53:05 EDT 2022

STATUS

editing

proposed

#37 by Vladimir Pletser at Fri Jul 15 23:50:17 EDT 2022

COMMENTS

Numbers A > 0 such that A = B^3 + (B+1)^3 = C^3 - D^3 and such that C - D = 3*(2*n - 1) == 3 (mod 6), with (for n > 1) C > D > B > 0, and A = as 27*t^3*(27*t^6 + 1)/4 with t = 2*n-1, and where A = a(n) (this sequence), B = A352760A355751(n), C = A352761A355752(n) and D = A352762A355753(n).

FORMULA

a(n) = A352760A355751(n)^3 + (A352760A355751(n) + 1)^3 = A352761A355752(n)^3 - A352762A355753(n)^3 and A352761A355752(n) - A352762A355753(n) = 3*(2*n - 1).

CROSSREFS

Cf. A005898, A001235, A272885, A352133, A352134, A352135, A352136, A352221, A352222, A352223, A352224, A352225, A352755, A352756, A352757, A352758, A352760, A352761, A352762A355751, A355752, A355753.

STATUS

approved

editing

Discussion

Fri Jul 15

23:53

Vladimir Pletser: Replaced A352760, A352761, A352762 by respectively A355751, A355752, A355753, due to reallocation of initially assigned A-numbers.

#36 by Michael De Vlieger at Mon Jul 11 16:09:28 EDT 2022

STATUS

reviewed

approved

#35 by Michel Marcus at Mon Jul 11 13:40:51 EDT 2022

STATUS

proposed

reviewed

#34 by Vladimir Pletser at Sun Jul 10 21:47:33 EDT 2022

STATUS

editing

proposed

#33 by Vladimir Pletser at Sun Jul 10 21:46:20 EDT 2022

NAME

Centered cube numbers that are the difference of two positive cubes; a(n) = 27*t^3*(27*t^6 + 1)/4 with t = 2*n-1.

COMMENTS

Numbers A > 0 such that A = B^3 + (B+1)^3 = C^3 - D^3 and such that C - D = 3*(2*n - 1) == 3 (mod 6), with (for n > 1) C > D > B, > 0, and A = as 27*t^3*(27*t^6 + 1)/4 with t = 2*n-1, and where A = a(n) (this sequence), B = A352760(n), C = A352761(n) and D = A352762(n).

LINKS

Vladimir Pletser, <a href="/A352759/b352759.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

Discussion

Sun Jul 10

21:47

Vladimir Pletser: @Prof. Sloane: Dear Prof. Sloane, thank you for your comments. It is indeed only positive integer cubes that are considered. I have modified the Name and Comments Sections accordingly. Thanks.
I have also appended a b-file.

#32 by N. J. A. Sloane at Sun Jul 10 16:01:43 EDT 2022

STATUS

proposed

approved

#31 by Jon E. Schoenfield at Thu Jun 02 01:04:47 EDT 2022

STATUS

editing

proposed

Discussion

Sun Jul 10

16:01

N. J. A. Sloane: Please see comments in A352755.

#30 by Jon E. Schoenfield at Thu Jun 02 01:04:44 EDT 2022

NAME

Centered cube numbers that are the difference of two cubes; a(n) = 27t27*t^3*(27t27*t^6 + 1)/4 with t = 2n2*n-1.

COMMENTS

Numbers A such that A = B^3 + (B+1)^3 = C^3 - D^3 and such that C - D = 3 *(2n 2*n - 1) == 3 (mod 6), with (for n > 1) C > D > B, and A = as 27t27*t^3*(27t27*t^6 + 1)/4 with t = 2n2*n-1, and where A = a(n) (this sequence), B = A352760(n), C = A352761(n) and D = A352762(n).

FORMULA

a(n) = A352760(n)^3 + (A352760(n) + 1)^3 = A352761(n)^3 - A352762(n)^3 and A352761(n) - A352762(n) = 3*(2n 2*n - 1).

a(n) = 27*(2n 2*n - 1)^3*(27*(2n 2*n - 1)^6 + 1)/4.

STATUS

proposed

editing