A085959 -id:A085959 - cp's OEIS frontend

A305548 a(n) = 27*n.

0, 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, 540, 567, 594, 621, 648, 675, 702, 729, 756, 783, 810, 837, 864, 891, 918, 945, 972, 999, 1026, 1053, 1080, 1107, 1134, 1161, 1188, 1215, 1242, 1269, 1296, 1323, 1350, 1377, 1404, 1431, 1458, 1485, 1512

Offset: 0

Eric Chen, Jun 05 2018

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

For a(n) = k*n: A001489 (k=-1), A000004 (k=0), A001477 (k=1), A005843 (k=2), A008585 (k=3), A008591 (k=9), A008607 (k=25), A252994 (k=26), this sequence (k=27), A135628 (k=28), A195819 (k=29), A249674 (k=30), A135631 (k=31), A174312 (k=32), A044102 (k=36), A085959 (k=37), A169823 (k=60), A152691 (k=64).

Mathematica
```
Range[0,2000,27]
```
PARI
```
a(n)=27*n
```

a(n) = 27*n.
a(n) = A008585(A008591(n)) = A008591(A008585(n)).
G.f.: 27*x/(x-1)^2.
From Elmo R. Oliveira, Apr 10 2025: (Start)
E.g.f.: 27*x*exp(x).
a(n) = 2*a(n-1) - a(n-2). (End)

A070189 a(n) = 12345679*n.

Original entry on oeis.org

0, 12345679, 24691358, 37037037, 49382716, 61728395, 74074074, 86419753, 98765432, 111111111, 123456790, 135802469, 148148148, 160493827, 172839506, 185185185, 197530864, 209876543, 222222222, 234567901, 246913580, 259259259, 271604938, 283950617, 296296296, 308641975

Offset: 0

Henry Bottomley, Apr 24 2002

a(82)=1012345678 is the first term which has a digit appearing more than once without an obvious pattern, although a(-82)=-1012345678 might be seen as the concatenation of ten consecutive numbers.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 12345679 at p. 188.

Tanya Khovanova, Recursive Sequences.
"TyYann", MegaFavNumbers: Lewis Carroll's Number, video (2020).
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A027889, A057932, A060073, A085959.

Table[12345679*n,{n,0,30}] (* or *) LinearRecurrence[{2,-1},{0,12345679},30] (* Harvey P. Dale, Oct 16 2015 *)

a(n)=12345679*n \\ Charles R Greathouse IV, Jan 09 2012

concat(0, Vec(12345679*x/(1-x)^2 + O(x^26))) \\ Elmo R. Oliveira, Jun 26 2025

a(n) = n*(10^(10-1)-1)/(10-1)^2.
From Elmo R. Oliveira, Jun 26 2025: (Start)
G.f.: 12345679*x/(1-x)^2.
E.g.f.: 12345679*x*exp(x).
a(n) = 333667*A085959(n).
a(n) = 2*a(n-1) - a(n-2). (End)

More terms from Elmo R. Oliveira, Jun 26 2025

A199799 Totatives of 111111.

Original entry on oeis.org

1, 2, 4, 5, 8, 10, 16, 17, 19, 20, 23, 25, 29, 31, 32, 34, 38, 40, 41, 43, 46, 47, 50, 53, 58, 59, 61, 62, 64, 67, 68, 71, 73, 76, 79, 80, 82, 83, 85, 86, 89, 92, 94, 95, 97, 100, 101, 103, 106, 107, 109, 113, 115, 116, 118, 122, 124, 125, 127, 128, 131, 134

Offset: 1

Reinhard Zumkeller, Nov 11 2011

a(n) and 111111 are coprime, 111111 = 3*7*11*13*37; empty intersections with A008585, A008593, A008595, or A085959; sequence is finite with 51840 terms, A000010(111111) = 51840, last term: a(51840) = 111110.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Repunit
Eric Weisstein's World of Mathematics, Totative

Cf. A109492 (divisors of 111111).

a199799 n = a199799_list !! (n-1)
a199799_list = [x | x <- [1..111111], gcd x 111111 == 1]

Select[Range[200],CoprimeQ[#,111111]&] (* Paolo Xausa, Sep 27 2023 *)

cp's OEIS Frontend

A305548 a(n) = 27*n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A070189 a(n) = 12345679*n.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A199799 Totatives of 111111.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica