A125835 -id:A125835 - cp's OEIS frontend

A125725 Numbers whose base-7 representation is 222....2.

0, 2, 16, 114, 800, 5602, 39216, 274514, 1921600, 13451202, 94158416, 659108914, 4613762400, 32296336802, 226074357616, 1582520503314, 11077643523200, 77543504662402, 542804532636816, 3799631728457714, 26597422099204000

Offset: 1

Zerinvary Lajos, Feb 02 2007

			base 7.......decimal
0..................0
2..................2
22................16
222..............114
2222.............800
22222...........5602
222222.........39216
2222222.......274514
22222222.....1921600
222222222...13451202
etc...........etc.

Davis Smith, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (8,-7).

Cf. A007310, A023000, A047522, A165759.

Cf. also A002276, A005610, A020988, A024023, A125831, A125835, A125857 for related or similarly constructed sequences.

List([1..25], n-> (7^(n-1) -1)/3); # G. C. Greubel, May 23 2019

[0] cat [n:n in [1..15000000]| Set(Intseq(n,7)) subset [2]]; // Marius A. Burtea, May 06 2019

[(7^(n-1)-1)/3: n in [1..25]]; // Marius A. Burtea, May 06 2019

Maple
```
seq(2*(7^n-1)/6, n=0..25);
```

FromDigits[#,7]&/@Table[PadLeft[{2},n,2],{n,0,25}]  (* Harvey P. Dale, Apr 13 2011 *)
(7^(Range[25]-1) - 1)/3 (* G. C. Greubel, May 23 2019 *)

vector(25, n, (7^(n-1)-1)/3) \\ Davis Smith, Apr 04 2019

[(7^(n-1) -1)/3 for n in (1..25)] # G. C. Greubel, May 23 2019

a(n) = (7^(n-1) - 1)/3 = 2*A023000(n-1).
a(n) = 7*a(n-1) + 2, with a(1)=0. - Vincenzo Librandi, Sep 30 2010
G.f.: 2*x^2 / ( (1-x)*(1-7*x) ). - R. J. Mathar, Sep 30 2013
From Davis Smith, Apr 04 2019: (Start)
A007310(a(n) + 1) = 7^(n - 1).
A047522(a(n + 1)) = -1*A165759(n). (End)
E.g.f.: (exp(7*x) - 7*exp(x) + 6)/21. - Stefano Spezia, Jan 12 2025

Offset corrected by N. J. A. Sloane, Oct 02 2010

A125834 Numbers that have exactly 15 representations as a product of two palindromes.

Original entry on oeis.org

4888884, 8896888, 13345332, 74732526, 100999899, 140732592, 179555376, 269130862, 295777482, 444888444, 734059326, 880968088, 978745768, 1032039008, 1183109928, 1321452132, 1399939992, 1548058512, 1614785172, 1886140256

Offset: 1

Farideh Firoozbakht, Dec 11 2006

			4888884 is in the sequence since 4888884 = 1*4888884 = 2*2444442 = 4*1222221 = 11*444444 = 22*222222 = 44*111111 = 111*44044 = 121*40404 = 222*22022 = 242*20202 = 444*11011 = 484*10101 = 1001*4884 = 1221*4004 = 2002*2442.

Cf. A002113, A116993, A125832, A125833, A125835.

f[n_]:=f[n]=Length[Select[Divisors[n],#<=n^(1/2)&&FromDigits[ Reverse[IntegerDigits[ # ]]]==#&&FromDigits[Reverse[IntegerDigits [n/# ]]]==n/#&]];Do[If[f[n]==15,Print[n]],{n,125000000}]

a(6)-a(20) from Donovan Johnson, Aug 05 2009

A155803 A023001 interleaved with 2A023001 and 4A023001.

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 9, 18, 36, 73, 146, 292, 585, 1170, 2340, 4681, 9362, 18724, 37449, 74898, 149796, 299593, 599186, 1198372, 2396745, 4793490, 9586980, 19173961, 38347922, 76695844, 153391689, 306783378, 613566756, 1227133513, 2454267026, 4908534052

Offset: 0

Paul Curtz, Jan 27 2009

A033138 with three zeros prepended. - Joerg Arndt, Mar 10 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,1,-2).

[Floor(2^n/7): n in [0..40]]; // Vincenzo Librandi, Sep 17 2011

A023001 := proc(n) (8^n-1)/7; end: A155803 := proc(n) RETURN( A023001(n),2*A023001(n),4*A023001(n)) ; end: L := [seq(A155803(n),n=0..30)] ; # R. J. Mathar, Jul 23 2009
seq(floor(2^n/7),n=0..30) # Mircea Merca, Dec 22 2010

CoefficientList[Series[x^3/(1-2 x-x^3+2 x^4), {x,0,50}],x]  (* Harvey P. Dale, Mar 13 2011 *)

a(3n) = A023001(n). a(3n+1) = 2*A023001(n) = A125835(n). a(3n+2) = 4*A023001(n).
a(n) = a(n-3)+2^(n-3) = a(n-3)+A000079(n-3). Here, a(.) can also be one of its higher order differences.
a(n) = 2*a(n-1)+a(n-3)-2*a(n-4). G.f.: x^3/((x-1)*(2*x-1)*(1+x+x^2)). [R. J. Mathar, Jul 23 2009]
a(n) = floor(2^n/7). [Mircea Merca, Dec 22 2010]

Edited and extended by R. J. Mathar, Jul 23 2009

A334076 a(n) = bitwise NOR of n and 2n.

Original entry on oeis.org

0, 0, 1, 0, 3, 0, 1, 0, 7, 4, 1, 0, 3, 0, 1, 0, 15, 12, 9, 8, 3, 0, 1, 0, 7, 4, 1, 0, 3, 0, 1, 0, 31, 28, 25, 24, 19, 16, 17, 16, 7, 4, 1, 0, 3, 0, 1, 0, 15, 12, 9, 8, 3, 0, 1, 0, 7, 4, 1, 0, 3, 0, 1, 0, 63, 60, 57, 56, 51, 48, 49, 48, 39, 36, 33, 32, 35, 32, 33

Offset: 0

Alois P. Heinz, Apr 13 2020

Exactly all bits that are 0 in both parameters (but not a leading 0 of both) are set to 1 in the output of bitwise NOR.

Alois P. Heinz, Table of n, a(n) for n = 0..32767
Wikipedia, Bitwise operation

Cf. A000079, A048724, A125835, A141032, A163617, A213370, A247648.

a:= n-> Bits[Nor](n, 2*n):
seq(a(n), n=0..127);

a(n) = my(x=bitor(n, 2*n)); bitneg(x, #binary(x)); \\ Michel Marcus, Apr 14 2020

def A334076(n):
    m = n|(2*n)
    return 0 if n == 0 else 2**(len(bin(m))-2)-1-m # Chai Wah Wu, Apr 14 2020

a(n) = 0 <=> n in { A247648 } union { 0 }.
a(n) = n-1 <=> n in { A000079 }.
a(n) = n/2 <=> n in { A125835 }.
a(n) = n*3/4 <=> n in { A141032 }.

cp's OEIS Frontend

A125725 Numbers whose base-7 representation is 222....2.

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A125834 Numbers that have exactly 15 representations as a product of two palindromes.

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A155803 A023001 interleaved with 2*A023001 and 4*A023001.

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A334076 a(n) = bitwise NOR of n and 2n.

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A155803 A023001 interleaved with 2A023001 and 4A023001.