A097261 -id:A097261 - cp's OEIS frontend

A097262 Numbers whose set of base 16 digits is {0,F}, where F base 16 = 15 base 10.

0, 15, 240, 255, 3840, 3855, 4080, 4095, 61440, 61455, 61680, 61695, 65280, 65295, 65520, 65535, 983040, 983055, 983280, 983295, 986880, 986895, 987120, 987135, 1044480, 1044495, 1044720, 1044735, 1048320, 1048335, 1048560, 1048575

Offset: 0

Ray Chandler, Aug 03 2004

n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 16 for every i.

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

Cf. A001196, A005823, A097251-A097261.

[n: n in [0..1110000] | Set(IntegerToSequence(n, 16)) subset {0, 15}]; // Vincenzo Librandi, Jun 05 2012

f[n_] := FromDigits[ IntegerDigits[n, 2] /. {1 -> 15}, 16]; Array[f, 32, 0] (* or *)
FromDigits[#, 16] & /@ Tuples[{0, 15}, 6] (* Harvey P. Dale, Sep 22 2011 *) (* or much slower *)
fQ[n_] := Union@ Join[{0, 15}, IntegerDigits[n, 16]] == {0, 15}; Select[ Range[0, 11000000 ], fQ] (* Robert G. Wilson v, May 12 2012 *)

a(n) = 15*A033052(n).

a(2n) = 16*a(n), a(2n+1) = a(2n)+15.

A033051 Numbers whose set of base 15 digits is {0,1}.

Original entry on oeis.org

0, 1, 15, 16, 225, 226, 240, 241, 3375, 3376, 3390, 3391, 3600, 3601, 3615, 3616, 50625, 50626, 50640, 50641, 50850, 50851, 50865, 50866, 54000, 54001, 54015, 54016, 54225, 54226, 54240, 54241, 759375, 759376, 759390, 759391, 759600

Offset: 0

Clark Kimberling

Sums of distinct powers of 15.

a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060. - Philippe Deléham, Oct 17 2011.

T. D. Noe, Table of n, a(n) for n = 0..1023
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.

Cf. A000695, A005836, A033042-A033052.

Row 14 of array A104257.

With[{k = 15}, Map[FromDigits[#, k] &, Tuples[{0, 1}, 6]]] (* Michael De Vlieger, Oct 28 2022 *)
FromDigits[#,15]&/@Tuples[{0,1},6] (* Harvey P. Dale, Sep 15 2024 *)

A033051(n, b=15)=subst(Pol(binary(n)),'x,b) \\ M. F. Hasler, Feb 01 2016

a(n) = Sum_{i=0..m} d(i)*15^i, where Sum_{i=0..m} d(i)*2^i is the base-2 representation of n.
a(n) = A097261(n)/14.
a(2n) = 15*a(n), a(2n+1) = a(2n)+1.
a(n) = Sum_{k>=0} A030308(n,k)*15^k. - Philippe Deléham, Oct 17 2011.
G.f.: (1/(1 - x))*Sum_{k>=0} 15^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017

Extended by Ray Chandler, Aug 03 2004

cp's OEIS Frontend

A097262 Numbers whose set of base 16 digits is {0,F}, where F base 16 = 15 base 10.

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