keyword:less - cp's OEIS frontend

A031045 Triangle T(n,k): write n in base 8, reverse order of digits.

0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5, 7, 5, 0, 6, 1

Offset: 0

Clark Kimberling

Robert Israel, Table of n, a(n) for n = 0..10003 (rows 0 to 3646, flattened)

Cf. A030308, A030341, A030386, A031235, A030567, A031007, A031087, A031298 for the base-2 to base-10 analogs.

seq(op(convert(n,base,8)),n=0..100); # Robert Israel, Jul 22 2019

Flatten[Table[Reverse[IntegerDigits[n,8]],{n,80}]] (* Harvey P. Dale, Aug 08 2011 *)

A031045(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.");*/n\8^k%8 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030341, ... Note: The operation could be done using bitwise arithmetic, bitand(n>>(3*k),7), but this is not significantly faster in PARI. - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A137583 Number of elements in the n-th period of the Janet periodic table of elements.

Original entry on oeis.org

2, 2, 8, 8, 18, 18, 32, 32

Offset: 1

Paul Curtz, Apr 26 2008

Essentially 2 followed by the first terms of A093907.

This puts Hydrogen and Helium in the first row, Lithium and Beryllium into the second, Boron to Magnesium into the third etc.

Mark R. Leach, The Internet Database of Periodic Tables, Chemogenesis web book.
Albert Tarantola, PSE of Elements (Janet form).
Mark J. Winter, Image of the Janet long format (or 32-column) periodic table, Web Elements Chemistry Nexus.

Cf. A093907, A137508, A138509, A137575.

Flatten@ Table[2 (n #)^2 & /@ {-1, 1}, {n, 4}] (* Michael De Vlieger, Jul 22 2016 *)

Edited by R. J. Mathar, Oct 02 2009

A201734 Numbers n such that 90*n + 47 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 9, 10, 13, 14, 16, 18, 20, 22, 24, 25, 27, 29, 31, 32, 38, 39, 43, 44, 49, 50, 51, 53, 56, 63, 64, 65, 66, 69, 77, 80, 83, 84, 87, 90, 91, 95, 98, 101, 102, 105, 106, 107, 108, 109, 111, 116, 118, 120, 121, 122, 123, 129, 132, 134, 135, 137

Offset: 1

J. W. Helkenberg, Dec 04 2011

A reverse reading of A142313; all entries of A142313 have digital root 2 and last digit 7.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007.

[n: n in [0..200] | IsPrime(90*n+47)]; // Vincenzo Librandi, Dec 11 2011

for n from 0 to 240 do
    p := 90*n+47 ;
    if isprime(p) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 05 2011

Select[Range[0,400],PrimeQ[90 #+47]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+47) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142313(n)-47)/90.

A031007 Triangle T(n,k): Write n in base 7, reverse order of digits, to get row n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5, 0, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6, 6, 6

Offset: 0

Clark Kimberling

Cf. A030308, A030341, A030386, A031235, A030567, A031045, A031087, A031298 for the base-2 to base-10 analogs.

Flatten[Table[Reverse[IntegerDigits[n,7]],{n,0,50}]] (* Harvey P. Dale, Feb 25 2014 *)

A031007(n, k=-1)={k<0&&error("Flattened sequence not yet implemented.");n\7^k%7} \\ Assuming that columns start with k=0 as in A030308, A030341, ... TO DO: implement flattened sequence, such that A030567(n)=a(n). - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A128393 Numbers k such that k^2 divides 13^k - 1.

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 14, 20, 28, 42, 60, 68, 84, 140, 183, 204, 220, 340, 366, 406, 420, 476, 660, 732, 812, 942, 1020, 1218, 1428, 1540, 1806, 1860, 1884, 2380, 2436, 2562, 3612, 3660, 3740, 4060, 4620, 5060, 5124, 6594, 7004, 7140, 8420, 9420, 9940, 11220

Offset: 1

Alexander Adamchuk, Mar 01 2007

Harvey P. Dale, Table of n, a(n) for n = 1..500

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Join[{1},Select[Range[12000],PowerMod[13,#,#^2]==1&]] (* Harvey P. Dale, Sep 05 2012 *)

A128397 Numbers k such that k^2 divides 17^k-1.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 36, 40, 42, 48, 60, 72, 78, 80, 84, 116, 120, 126, 144, 156, 168, 180, 220, 232, 234, 240, 252, 312, 336, 342, 348, 360, 420, 440, 464, 468, 504, 546, 580, 624, 660, 684, 696, 720, 780, 840, 880, 936, 1008, 1044, 1092, 1160

Offset: 1

Alexander Adamchuk, Mar 01 2007

The first 9 numbers (and many more) which are a multiple of their digital sum in all bases from 2 through 16 (A218087), are members of this sequence, and also of A177917. - M. F. Hasler, Oct 22 2012

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Cf. A177917.

is_A128397(n)=Mod(17,n^2)^n==1  \\ M. F. Hasler, Oct 22 2012

A137752 First numerator and then denominator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 3, 5, 6, 1, 3, 1, 4, 7, 12, 7, 12, 1, 4, 1, 5, 9, 20, 31, 30, 9, 20, 1, 5, 1, 6, 11, 30, 49, 60, 49, 60, 11, 30, 1, 6, 1, 7, 13, 42, 71, 105, 209, 140, 71, 105, 13, 42, 1, 7, 1, 8, 15, 56, 97, 168, 351, 280, 351, 280, 97, 168

Offset: 1

Mohammad K. Azarian, Feb 10 2008

In this triangle the right-hand edge consists of the reciprocals of the positive integers. A number that is not in this edge is obtained by adding the number diagonally above it to the number to its immediate right. Note that in Leibniz's harmonic triangle we subtract the two numbers to get a number which is not on the right-hand edge.

			1/1;
1/2, 1/2;
1/3, 5/6, 1/3;
1/4, 7/12, 7/12, 1/4;
1/5, 9/20, 31/30, 9/20, 1/5;

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212.

Cf. A137753

A137753 First denominator and then numerator (left to right) of Leibniz's harmonic-like triangle.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 3, 1, 6, 5, 3, 1, 4, 1, 12, 7, 12, 7, 4, 1, 5, 1, 20, 9, 30, 31, 20, 9, 5, 1, 6, 1, 30, 11, 60, 49, 60, 49, 30, 11, 6, 1, 7, 1, 42, 13, 105, 71, 140, 209, 105, 71, 42, 13, 7, 1, 8, 1, 56, 15, 168, 97, 280, 351, 280, 351, 168, 97

Offset: 1

Mohammad K. Azarian, Feb 10 2008

			1/1; --> 1 1
1/2, 1/2; --> 2 1 2 1
1/3, 5/6, 1/3; --> 3 1 6 5 3 1
1/4, 7/12, 7/12, 1/4; --> 4 1 12 7 12 7 4 1
1/5, 9/20, 31/30, 9/20, 1/5; --> 5 1 20 9 30 31 20 9 5 1

Cf. A003506; A007622; A046201; A046204; A046205; A046206; A046208; A046212; A137752.

Cf. A137752

A139198 a(n) = prime(n)!/10 - 1.

Original entry on oeis.org

11, 503, 3991679, 622702079, 35568742809599, 12164510040883199, 2585201673888497663999, 884176199373970195454361599999, 822283865417792281772556287999999

Offset: 3

Artur Jasinski, Apr 11 2008

Cf. A039716, A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197.

Mathematica
```
Table[(Prime[n]! - 10)/10, {n, 3, 20}]
```

a(n) = prime(n)!/10 - 1 \\ David A. Corneth, Jun 02 2017

a(n) = A039716(n)/10 - 1. - Elmo R. Oliveira, Jan 20 2023

A115341 a(n) = abs(A154879(n+1)).

Original entry on oeis.org

2, 4, 0, 8, 8, 24, 40, 88, 168, 344, 680, 1368, 2728, 5464, 10920, 21848, 43688, 87384, 174760, 349528, 699048, 1398104, 2796200, 5592408, 11184808, 22369624, 44739240, 89478488, 178956968, 357913944, 715827880, 1431655768, 2863311528

Offset: 0

Roger L. Bagula, Mar 06 2006

General form: a(n)=2^n-a(n-1). - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

For n>=1, a(n) is a(n) is the number of generalized compositions of n+3 when there are i^2-2*i-1 different types of i, (i=1,2,...). - Milan Janjic, Sep 24 2010

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

Cf. A001045, A078008, A097073. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

[2] cat [(2^(n+1)-8*(-1)^n)/3: n in [1..30]]; // G. C. Greubel, Dec 30 2017

g0[n_] = 2 - Sum[(-1)^(i + 1)/Sqrt[2]^(2*i), {i, 0, n}] f[x_] = ZTransform[g0[n], n, x] g[n_] = InverseZTransform[f[1/x], x, n] a0 = Table[Abs[g[n]], {n, 1, 25}]
k=0;lst={k};Do[k=2^n-k;AppendTo[lst, k], {n, 3, 5!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
Table[If[n==0, 2, (2^(n+1)-8*(-1)^n)/3], {n,0,30}] (* G. C. Greubel, Dec 30 2017 *)

for(n=0,30, print1(if(n==0, 2, (2^(n+1)-8*(-1)^n)/3), ", ")) \\ G. C. Greubel, Dec 30 2017

a(n) = (2^(n+1)-8*(-1)^n)/3, n>0.
a(n) = a(n-1) + 2*a(n-2), n>2.
G.f.: 2+4*x*(1-x)/((1+x)*(1-2*x)).

Edited by the Associate Editors of the OEIS, Aug 21 2009

cp's OEIS Frontend

A031045 Triangle T(n,k): write n in base 8, reverse order of digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A137583 Number of elements in the n-th period of the Janet periodic table of elements.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A201734 Numbers n such that 90*n + 47 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A031007 Triangle T(n,k): Write n in base 7, reverse order of digits, to get row n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Extensions

A128393 Numbers k such that k^2 divides 13^k - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A128397 Numbers k such that k^2 divides 17^k-1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A137752 First numerator and then denominator (left to right) of Leibniz's harmonic-like triangle.

Views

Author

Keywords

Comments

Examples

Crossrefs

A137753 First denominator and then numerator (left to right) of Leibniz's harmonic-like triangle.

Views

Author

Keywords

Examples

Crossrefs

A139198 a(n) = prime(n)!/10 - 1.

Views

Author

Keywords

Crossrefs

Programs