login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279816 Digital roots of tetrahedral numbers (A000292). 0
0, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Period 27: repeat [1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9, 9, 9] for n >= 1.

LINKS

Table of n, a(n) for n=0..108.

Eric Weisstein's World of Mathematics, Digital Root

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1,0,-1,1).

FORMULA

G.f.: x*(1 + 4*x + x^2 + 2*x^3 + 8*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 3*x^8 + 4*x^9 + 7*x^10 + 4*x^11 + 5*x^12 + 2*x^13 + 5*x^14 + 6*x^15 + 6*x^16 + 6*x^17 + 7*x^18 + x^19 + 7*x^20 + 8*x^21 + 5*x^22 + 8*x^23 + 9*x^24 + 9*x^25 + 9*x^26)/(1 - x^27).

a(n) = A010888(A000292(n)).

EXAMPLE

a(6) = 2 because the 6th tetrahedral number is 56, 5 + 6 = 11 -> 1 + 1 = 2.

MATHEMATICA

Join[{0}, Table[n (n + 1) (n + 2)/6 - 9 Floor[(n - 1) (n^2 + 4 n + 6)/54], {n, 108}]]

Join[{0}, LinearRecurrence[{1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1}, {1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 9}, 108]]

CROSSREFS

Cf. A000292, A004160, A010888, A145389.

Sequence in context: A096249 A081454 A133883 * A004160 A128077 A128078

Adjacent sequences:  A279813 A279814 A279815 * A279817 A279818 A279819

KEYWORD

nonn,base,easy

AUTHOR

Ilya Gutkovskiy, Dec 19 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 00:15 EDT 2019. Contains 321306 sequences. (Running on oeis4.)