The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115872 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A115872

Square array where row n gives all solutions k > 0 to the cross-domain congruence n*k = A048720(A065621(n),k), zero sequence (A000004) if no such solutions exist.
(history; published version)

#24 by Michael De Vlieger at Tue Jan 04 09:22:49 EST 2022

STATUS

reviewed

approved

#23 by Michel Marcus at Tue Jan 04 09:09:49 EST 2022

STATUS

proposed

reviewed

#22 by Jean-François Alcover at Tue Jan 04 08:33:48 EST 2022

STATUS

editing

proposed

#21 by Jean-François Alcover at Tue Jan 04 08:33:37 EST 2022

MATHEMATICA

X[a_, b_] := Module[{A, B, C, x},

A = Reverse@IntegerDigits[a, 2];

B = Reverse@IntegerDigits[b, 2];

C = Expand[

Sum[A[[i]]*x^(i-1), {i, 1, Length[A]}]*

Sum[B[[i]]*x^(i-1), {i, 1, Length[B]}]];

PolynomialMod[C, 2] /. x -> 2];

T[n_, k_] := Module[{x = BitXor[n-1, 2n-1], k0 = k},

For[i = 1, True, i++, If[n*i == X[x, i],

If[k0 == 1, Return[i], k0--]]]];

Table[T[n-k+1, k], {n, 1, 14}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 04 2022 *)

STATUS

approved

editing

#20 by Susanna Cuyler at Tue May 28 19:34:24 EDT 2019

STATUS

proposed

approved

#19 by Antti Karttunen at Fri May 24 15:04:37 EDT 2019

STATUS

editing

proposed

#18 by Antti Karttunen at Wed May 15 11:23:24 EDT 2019

COMMENTS

Rows at positions 2^k are 1, 2, 3, ..., (A000027). Row 2n is equal to row n.

CROSSREFS

Rows at positions 2^k are A000027. Row at the position 2n is equal to the row at position n.

Discussion

Wed May 22

19:04

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A115872 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Fri May 24

14:44

Antti Karttunen: The escape-clause is very likely unnecessary, but I will return to this one after my mind finds itself back to this particular zone.

#17 by Antti Karttunen at Fri May 10 07:46:58 EDT 2019

PROG

A000265(n) = (n/2^valuation(n, 2));

A006519(n) = (1<<valuation(n, 2));

A048720(b, c) = if(!b || !c, 0, if(!(b%2), A006519(b)*A048720(A000265(b), c), bitxor(c, 2*A048720((b-1)/2, c))));

\\ A048720 can be computed also as:

A115872(n) = v115872[n]; \\ (Slow, but does the job! ) - Antti Karttunen, May 08 2019

#16 by Antti Karttunen at Fri May 10 07:45:53 EDT 2019

PROG

\\ A048720 can be computed also as:

A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);

#15 by Antti Karttunen at Fri May 10 04:46:16 EDT 2019

CROSSREFS

Cf. A048720, A065621, A115857, A115871, A325565, A325566, A325567, A325568, A325570, A325571.