A225374 -id:A225374 - cp's OEIS frontend

A100401 Digital root of 3^n.

1, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Cino Hilliard, Dec 30 2004

This sequence also gives the digital root of 12^n, 21^n, 30^n, 39^n, 48^n, 57^n, ... (any k^n where k is congruent to 3 mod 9). - Timothy L. Tiffin, Dec 02 2023

			For n=14, the digits of 3^14 = 4782969 sum to 45, whose digits sum to 9. So, a(14) = 9.

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A000244, A001021, A007953, A009965, A009974, A009983, A009992, A010888, A100403, A225374.

Table[PowerMod[3, n, 18], {n, 0, 100}] (* Timothy L. Tiffin, Dec 03 2023 *)
PadRight[{1,3}, 100, 9] (* Timothy L. Tiffin, Dec 03 2023 *)

a(n) = if( n<2, [1,3][n+1], 9); \\ Joerg Arndt, Dec 03 2023

[power_mod(3,n,18) for n in range(105)] # Zerinvary Lajos, Nov 25 2009

a(n) = 3^n mod 18. - Zerinvary Lajos, Nov 25 2009
From Timothy L. Tiffin, Nov 30 2023: (Start)
a(n) = 9 for n >= 2.
G.f.: (1+2x+6x^2)/(1-x).
a(n) = A100403(n) for n <> 1. (End)
a(n) = A010888(A000244(n)). - Michel Marcus, Dec 01 2023
a(n) = A010888(A001021(n)) = A010888(A009965(n)) = A010888(A009974(n)) = A010888(A009983(n)) = A010888(A009992(n)) = A010888(A225374(n)). - Timothy L. Tiffin, Dec 02 2023
E.g.f.: 9*exp(x) - 6*x - 8. - Elmo R. Oliveira, Aug 08 2024
a(n) = A007953(3*a(n-1)) = A010888(3*a(n-1)). - Stefano Spezia, Mar 20 2025

A291945 Powers of 1111.

Original entry on oeis.org

1, 1111, 1234321, 1371330631, 1523548331041, 1692662195786551, 1880547699518858161, 2089288494165451416871, 2321199517017816524143681, 2578852663406794158323629591, 2865105309044948309897552475601, 3183131998348937572296180800392711, 3536459650165669642821056869236301921, 3929006671334058973174194181721531434231

Offset: 0

Seiichi Manyama, Mar 09 2018

Index entries for linear recurrences with constant coefficients, signature (1111).

Powers of ((10^k - 1)/9): A000012 (k=1), A001020 (k=2), A225374 (k=3), this sequence (k=4), A291946 (k=5), A109716 (k=6).

Cf. A096884.

1111^Range[0,20] (* Harvey P. Dale, Jul 27 2022 *)

a(n) = 1111^n; \\ Michel Marcus, Mar 11 2018

a(n) = 1111^n.
G.f.: 1/(1 - 1111*x).
From Elmo R. Oliveira, Aug 16 2024: (Start)
E.g.f.: exp(1111*x).
a(n) = 1111*a(n-1) for n > 0.
a(n) = A001020(n)*A096884(n). (End)

A291946 Powers of 11111.

Original entry on oeis.org

1, 11111, 123454321, 1371700960631, 15240969373571041, 169342410709747836551, 1881563525396008211918161, 20906052330675047242622686871, 232287147446130449912780673823681, 2580942495273955428980906066854919591, 28676852064988918771406847308825011575601, 318628503294091876469101480448354703616502711

Offset: 0

Seiichi Manyama, Mar 09 2018

Index entries for linear recurrences with constant coefficients, signature (11111).

Powers of ((10^k - 1)/9): A000012 (k=1), A001020 (k=2), A225374 (k=3), A291945 (k=4), this sequence (k=5), A109716 (k=6).

Cf. A009985.

my(x='x+O('x^99)); Vec(1/(1-11111*x)) \\ Altug Alkan, Mar 10 2018

a(n) = 11111^n.
G.f.: 1/(1 - 11111*x).
From Elmo R. Oliveira, Aug 26 2024: (Start)
E.g.f.: exp(11111*x).
a(n) = 11111*a(n-1) for n > 0.
a(n) = 271^n * A009985(n). (End)

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A100401 Digital root of 3^n.

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A291945 Powers of 1111.

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A291946 Powers of 11111.

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