A010706 -id:A010706 - cp's OEIS frontend

A195035 Multiples of 15 and of 8 interleaved: a(2n-1) = 15n, a(2n) = 8n.

15, 8, 30, 16, 45, 24, 60, 32, 75, 40, 90, 48, 105, 56, 120, 64, 135, 72, 150, 80, 165, 88, 180, 96, 195, 104, 210, 112, 225, 120, 240, 128, 255, 136, 270, 144, 285, 152, 300, 160, 315, 168, 330, 176, 345, 184, 360, 192, 375, 200, 390, 208, 405, 216

Offset: 1

Omar E. Pol, Sep 12 2011

First differences of A195036.

a(n) is also the length of the n-th edge of a square spiral in which the first two edges are the legs of the primitive Pythagorean triple [15, 8, 17]. Zero together with partial sums give A195036; the vertices of the spiral.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Ron Knott, Pythagorean triangles and Triples
Eric Weisstein's World of Mathematics, Pythagorean Triple
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A004526, A010686, A010706.

Cf. A195019, A195031, A195033, A195036.

&cat[[15*n, 8*n]: n in [1..27]];  // Bruno Berselli, Sep 30 2011

Riffle[15*#, 8*#] & [Range[50]] (* Paolo Xausa, Mar 21 2024 *)

a(n)=(n+1)\2*if(n%2,15,8) \\ Charles R Greathouse IV, Oct 07 2015

From Bruno Berselli, Sep 30 2011: (Start)
G.f.: x*(15+8*x)/((1-x)^2*(1+x)^2).
a(n) = A010686(n)*A010706(n-1)*A004526(n+1) = (23*n-(7*n+15)*(-1)^n+15)/4.
a(n) = 2*a(n-2) - a(n-4).
a(-n) = -a(A014681(n-1)). (End)

A243520 Numbers that are congruent to {0, 8} mod 11.

Original entry on oeis.org

0, 8, 11, 19, 22, 30, 33, 41, 44, 52, 55, 63, 66, 74, 77, 85, 88, 96, 99, 107, 110, 118, 121, 129, 132, 140, 143, 151, 154, 162, 165, 173, 176, 184, 187, 195, 198, 206, 209, 217, 220, 228, 231, 239, 242, 250, 253, 261, 264, 272, 275, 283, 286, 294, 297, 305

Offset: 0

Viet Quoc Le Tran, Jun 14 2014

Union of A008593 and A017485. - Michel Marcus, Jun 15 2014

This sequence mimics in some sense the ceiling function of n/2 (the seq. A110654) relative to variations from a main class of recurrence relations; in order to get the ceiling function of n/2 (see Formula section), the vector v must be [0,1] instead of [3,8]. - R. J. Cano, Jun 15 2014

R. J. Cano, Table of n, a(n) for n = 0..9999
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A010706, A110654, A078707.

&cat [[11*n,11*n+8]: n in [0..30]]; // [Bruno Berselli, Jun 16 2014]

A243520:=n->5*n + 2*(n mod 2) + ceil(n/2); seq(A243520(n), n=0..50); # Wesley Ivan Hurt, Jun 21 2014

Flatten[Table[11 n + {0, 8}, {n, 0, 32}]] (* Alonso del Arte, Jun 15 2014 *)

a(n)=5*n+2*(n%2)+ceil(n/2); \\ R. J. Cano, Jun 15 2014

a(n)=if(!n,0,a(n-1)+[3,8][1+n%2]); \\ R. J. Cano, Jun 15 2014

a(n) = -5/4*(-1)^n + 11*n/2 + 5/4.
From R. J. Cano, Jun 15 2014: (Start)
a(n) = 5*n + 2*(n mod 2) + ceiling(n/2).
If n=0 then a(n) is zero, else a(n) = a(n-1) + v[n mod 2], where v is [3,8]. (End)
G.f.: x*(8 + 3*x) / ((1 + x)*(1 - x)^2). [Bruno Berselli, Jun 16 2014]
a(n) = sum( A010706(i), i=0..n ) - 3. [Bruno Berselli, Jun 16 2014]
E.g.f.: (11*x*exp(x) + 5*sinh(x))/2. - David Lovler, Sep 04 2022

A176107 Decimal expansion of (6+sqrt(42))/4.

Original entry on oeis.org

3, 1, 2, 0, 1, 8, 5, 1, 7, 4, 6, 0, 1, 9, 6, 5, 0, 5, 7, 7, 4, 1, 4, 9, 1, 8, 5, 9, 0, 2, 1, 9, 9, 9, 1, 6, 4, 4, 2, 6, 3, 0, 1, 0, 7, 6, 7, 6, 4, 5, 8, 6, 6, 3, 7, 4, 2, 7, 8, 3, 8, 5, 9, 9, 4, 5, 2, 4, 0, 4, 3, 4, 4, 4, 6, 1, 0, 1, 1, 0, 9, 2, 8, 5, 0, 0, 9, 0, 2, 2, 6, 6, 5, 1, 4, 0, 2, 5, 5, 8, 9, 1, 8, 8, 6

Offset: 1

Klaus Brockhaus, Apr 10 2010

Continued fraction expansion of (6+sqrt(42))/4 is A010706.

			(6+sqrt(42))/4 = 3.12018517460196505774...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010496 (decimal expansion of sqrt(42)), A010706 (repeat 3, 8).

RealDigits[(6+Sqrt[42])/4,10,120][[1]] (* Harvey P. Dale, Jun 22 2012 *)

A176454 Decimal expansion of (12+2*sqrt(42))/3.

Original entry on oeis.org

8, 3, 2, 0, 4, 9, 3, 7, 9, 8, 9, 3, 8, 5, 7, 3, 4, 8, 7, 3, 1, 0, 6, 4, 4, 9, 5, 7, 3, 9, 1, 9, 9, 7, 7, 7, 1, 8, 0, 3, 4, 6, 9, 5, 3, 8, 0, 3, 8, 8, 9, 7, 6, 9, 9, 8, 0, 7, 5, 6, 9, 5, 9, 8, 5, 3, 9, 7, 4, 4, 9, 1, 8, 5, 6, 2, 6, 9, 6, 2, 4, 7, 6, 0, 0, 2, 4, 0, 6, 0, 4, 4, 0, 3, 7, 4, 0, 1, 5, 7, 1, 1, 6, 9, 6

Offset: 1

Klaus Brockhaus, Apr 20 2010

Continued fraction expansion of (12+2*sqrt(42))/3 is A010706 preceded by 8.

			(12+2*sqrt(42))/3 = 8.32049379893857348731...

Cf. A010496 (decimal expansion of sqrt(42)), A010706 (repeat 3, 8).

RealDigits[(12+2*Sqrt[42])/3,10,120][[1]] (* Harvey P. Dale, Nov 23 2016 *)

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A195035 Multiples of 15 and of 8 interleaved: a(2n-1) = 15n, a(2n) = 8n.

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A243520 Numbers that are congruent to {0, 8} mod 11.

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A176107 Decimal expansion of (6+sqrt(42))/4.

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A176454 Decimal expansion of (12+2*sqrt(42))/3.

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