A014832 -id:A014832 - cp's OEIS frontend

A048441 Take the first n numbers written in base 9, concatenate them, then convert from base 9 to base 10.

1, 11, 102, 922, 8303, 74733, 672604, 6053444, 490328973, 39716646823, 3217048392674, 260580919806606, 21107054504335099, 1709671414851143033, 138483384602942585688, 11217154152838349440744, 908589486379906304700281, 73595748396772410680722779

Offset: 1

Patrick De Geest, May 15 1999

The first two primes in this sequence occur for n = 2 (a(2) = 11) and n = 14 (a(14) = 1709671414851143033) (email from Kurt Foster, Oct 24 2015). - N. J. A. Sloane, Oct 25 2015

			a(9) = (1)(2)(3)(4)(5)(6)(7)(8)(10) = 1234567810_9 = 490328973.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A014832, A055150.

Concatenation of first n numbers in other bases: 2: A047778, 3: A048435, 4: A048436, 5: A048437, 6: A048438, 7: A048439, 8: A048440, 9: this sequence, 10: A007908, 11: A048442, 12: A048443, 13: A048444, 14: A048445, 15: A048446, 16: A048447.

[n eq 1 select 1 else Self(n-1)*9^(1+Ilog(9, n))+n: n in [1..20]]; // Vincenzo Librandi, Dec 30 2012

If[STARTPOINT==1, n={}, n=Flatten[IntegerDigits[Range[STARTPOINT-1], 9]]]; Table[AppendTo[n, IntegerDigits[w, 9]]; n=Flatten[n]; FromDigits[n, 9], {w, STARTPOINT, ENDPOINT}] (* Dylan Hamilton, Aug 11 2010 *)
f[n_]:= FromDigits[Flatten@IntegerDigits[Range@n, 9], 9]; Array[f, 20] (* Vincenzo Librandi, Dec 30 2012 *)

{ cuo=0;
for(ixp=1, 18,
casi = ixp; cvst=0;
while(casi != 0,
cvd = casi%9; cvst=10*cvst + cvd + 1; casi = (casi - cvd) / 9 );
while(cvst !=0, ptch = cvst%10;
cuo=cuo*9+ptch-1; cvst = (cvst - ptch) / 10 ); print1(cuo, ", "))}
\\ Douglas Latimer, Apr 27 2012

More terms from Douglas Latimer, May 10 2012

A353100 a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n.

Original entry on oeis.org

8, 79, 717, 6458, 58126, 523137, 4708235, 42374116, 381367044, 3432303395, 30890730553, 278016574974, 2502149174762, 22519342572853, 202674083155671, 1824066748401032, 16416600735609280, 147749406620483511, 1329744659584351589, 11967701936259164290

Offset: 1

Seiichi Manyama, Apr 23 2022

Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Cf. A064617, A353094, A353095, A353096, A353097, A353098, A353099.

Cf. A014832.

LinearRecurrence[{11, -19, 9}, {8, 79, 717}, 20] (* Amiram Eldar, Apr 23 2022 *)

my(N=30, x='x+O('x^N)); Vec(x*(8-9*x)/((1-x)^2*(1-9*x)))

PARI
```
a(n) = (7*9^(n+1)+8*n-63)/64;
```

b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 9);

G.f.: x * (8 - 9 * x)/((1 - x)^2 * (1 - 9 * x)).
a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
a(n) = 7 * A014832(n) + n.
a(n) = (7*9^(n+1) + 8*n - 63)/64.
a(n) = Sum_{k=0..n-1} (9 - n + k)*9^k.
E.g.f.: exp(x)*(63*(exp(8*x) - 1) + 8*x)/64. - Stefano Spezia, May 29 2023

A002754 Related to coefficient of m in Jacobi elliptic function cn(z, m).

Original entry on oeis.org

0, 0, 4, 44, 408, 3688, 33212, 298932, 2690416, 24213776, 217924020, 1961316220, 17651846024, 158866614264, 1429799528428, 12868195755908, 115813761803232, 1042323856229152, 9380914706062436, 84428232354561996, 759854091191058040

Offset: 0

N. J. A. Sloane

A. Cayley, An Elementary Treatise on Elliptic Functions. Bell, London, 1895, p. 56.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Roland Bacher and Philippe Flajolet, Pseudo-factorials, elliptic functions, and continued fractions, arXiv:0901.1379 [math.CA], 2009.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
A. Cayley, An Elementary Treatise on Elliptic Functions (page images), G. Bell and Sons, London, 1895, p. 56.
G. Viennot, Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi, J. Combin. Theory, A 29 (1980), 121-133.
J. Tannery and J. Molk, Eléments de la Théorie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 92.
Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Cf. A060627, A014832.

[(9^n-8*n-1)/16: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

a[ n_] := If[ n < 0, 0, (-1)^n (2 n)! Coefficient[ SeriesCoefficient[ JacobiCN[x, m], {x, 0, 2 n}], m, 1]]; (* Michael Somos, Dec 27 2014 *)
LinearRecurrence[{11, -19, 9}, {0, 0, 4}, 21] (* Jean-François Alcover, Sep 21 2017 *)

{a(n) = (9^n - 8*n -1) / 16}; /* Michael Somos, Jun 27 2003 */

From Michael Somos, Jun 27 2003: (Start)
G.f.: 4*x^2/((1-x)^2*(1-9*x)).
a(n) = (9^n-8*n-1)/16. (End)
a(n+2) = 4*A014832(n+1). [Bruno Berselli, Jun 29 2011]

More terms from Paolo Dominici (pl.dm(AT)libero.it) using formulas 16.22.1 and 16.22.2 of Abramowitz and Stegun's Handbook of Mathematical Functions.

cp's OEIS Frontend

A048441 Take the first n numbers written in base 9, concatenate them, then convert from base 9 to base 10.

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A353100 a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n.

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A002754 Related to coefficient of m in Jacobi elliptic function cn(z, m).

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A014857 Numbers k that divide s(k), where s(1)=1, s(j)=9*s(j-1)+j.

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