A036213 -id:A036213 - cp's OEIS frontend

A036215 Binary reversal of 3^n.

1, 3, 9, 27, 69, 207, 621, 3345, 4275, 25497, 38247, 229173, 589185, 1669443, 5205897, 14045019, 34319397, 102566511, 307313949, 1843835217, 2312645619, 13776780249, 20417442711, 112792132341, 290155405761, 847524815523, 2611222884297, 7627711248315

Offset: 0

Antti Karttunen

Compute 3^n in binary, reverse the bits, from 0 to the most significant bit of the power.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A036213 and A036214.

Table[FromDigits[Reverse[IntegerDigits[3^n, 2]], 2], {n, 0, 30}] (* Vincenzo Librandi, Sep 09 2013 *)

a(n) = subst(Polrev(binary(3^n)), x, 2); \\ Michel Marcus, Sep 08 2013

a(n) = A030101(A000244(n)). - Michel Marcus, Sep 08 2013

More terms from Michel Marcus, Sep 08 2013

A036214 Bit-reversing masks for 2*n bits.

Original entry on oeis.org

0, 18, 4740, 17966088, 1136090292240, 1171507928472027168, 19496308761789043518734400, 5212738348288268369644435170918528, 22344471816287582119092726913736555148345600, 1533995044405866391626076022957811770200509055768723968

Offset: 0

Antti Karttunen

R. Schroeppel: DECsystem-10/20 Processor Reference Manual AA-H391A-TK, Chapter 2, User Operations, section 2.15: Programming Examples: Reversing Order of Digits.

M. Beeler, R. W. Gosper, and R. Schroeppel, A Bit-Reversing Example in HAKMEM (Item 167).
Bitsavers, DECsystem-10 DECSYSTEM-20 Processor Reference Manual AA-H391A-TK, Fifth Edition, July 1980 (Updated, June 1982). (Section 2.15, Programming Examples, example "Reversing Order of Digits" on p. 2-116, page 177 of PDF)
Antti Karttunen, A Simple C program Demonstrating Bit Reversals.
Index entries for sequences related to binary expansion of n.

Cf. A036213, A036215.

Table[2^n*(2^(2*n^2 + 3*n + 1) + 2^(2*n^2 + 2*n) - 2^(3*n + 1) - 1)/(2^(2*n + 1) - 1), {n, 0, 10}] (* Wesley Ivan Hurt, Jun 10 2024 *)

A036214(n) = 2^n * ( 2^(2*n^2+3*n+1) + 2^(2*n^2+2*n) - 2^(3*n+1) - 1 ) / (2^(2*n+1) - 1); \\ Antti Karttunen, Jan 14 2024

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

log(a(n)) ~ log(4) * n ^ 2. - Bill McEachen, Jul 13 2024

cp's OEIS Frontend

A036215 Binary reversal of 3^n.

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