The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A301479 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A301479

Positive integers m such that m^3 cannot be written in the form x^2 + 2*y^2 + 3*2^z with x,y,z nonnegative integers.
(history; published version)

#17 by Bruno Berselli at Thu Mar 22 09:46:37 EDT 2018

STATUS

proposed

approved

#16 by Zhi-Wei Sun at Thu Mar 22 08:26:11 EDT 2018

STATUS

editing

proposed

#15 by Zhi-Wei Sun at Thu Mar 22 08:25:13 EDT 2018

MATHEMATICA

tab={}; Do[Do[If[QQ[m^3-3*2^k], Goto[aa]], {k, 0, Log[2, m^3/3]}]; tab=Append[tab, m]; Label[aa], {m, 1, 295429}]; Print[tab]

STATUS

proposed

editing

Discussion

Thu Mar 22

08:26

Zhi-Wei Sun: Okay, I modify the program to use terms not greater than 429.

#14 by Michel Marcus at Thu Mar 22 08:16:59 EDT 2018

STATUS

editing

proposed

#13 by Michel Marcus at Thu Mar 22 08:16:40 EDT 2018

DATA

1, 53, 69, 71, 77, 87, 101, 103, 106, 117, 127, 133, 138, 142, 149, 159, 173, 174, 181, 191, 197, 199, 202, 206, 207, 212, 213, 221, 223, 229, 231, 234, 266, 269, 276, 277, 284, 293, 298, 309, 311, 325, 341, 346, 348, 351, 357, 362, 365, 373, 389, 398, 404, 412, 423, 424, 426, 429

STATUS

proposed

editing

Discussion

Thu Mar 22

08:16

Michel Marcus: no, I already did it, didn't you see ?

#12 by Zhi-Wei Sun at Thu Mar 22 08:05:25 EDT 2018

STATUS

editing

proposed

#11 by Zhi-Wei Sun at Thu Mar 22 08:04:16 EDT 2018

COMMENTS

It is known that a positive integer n has the form x^2 + 2*y^2 with x and y integers if and only if the p-adic order of n is even for any prime p == 5 or 7 (mod 8).

Discussion

Thu Mar 22

08:05

Zhi-Wei Sun: Dear Michel,

   I have done that. Thank you!

    -- Zhi-Wei Sun

#10 by Zhi-Wei Sun at Thu Mar 22 08:02:22 EDT 2018

DATA

MATHEMATICA

tab={}; Do[Do[If[QQ[m^3-3*2^k], Goto[aa]], {k, 0, Log[2, m^3/3]}]; tab=Append[tab, m]; Label[aa], {m, 1, 585295}]; Print[tab]

STATUS

proposed

editing

#9 by Michel Marcus at Thu Mar 22 07:52:02 EDT 2018

STATUS

editing

proposed

#8 by Michel Marcus at Thu Mar 22 07:51:42 EDT 2018

DATA

MATHEMATICA

f[n_]:=f[n]=FactorInteger[n];

STATUS

proposed

editing

Discussion

Thu Mar 22

07:52

Michel Marcus: Please 3 lines and a half approx