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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052224 Numbers whose sum of digits is 10. 44
19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316, 325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 505, 514, 523, 532, 541, 550, 604, 613, 622, 631, 640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Proper subsequence of A017173. - Rick L. Shepherd, Jan 12 2009

Subsequence of A227793. - Michel Marcus, Sep 23 2013

A007953(a(n)) = 10; number of repdigits = #{55,22222,1^10} = A242627(10) = 3. - Reinhard Zumkeller, Jul 17 2014

a(n) = A094677(n) for n = 1..28. - Reinhard Zumkeller, Nov 08 2015

The number of terms having <= m digits is the coefficient of x^10 in sum(i=0,9,x^i)^m = ((1-x^10)/(1-x))^m. - David A. Corneth, Jun 04 2016

In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016

LINKS

T. D. Noe, Table of n, a(n) for n = 1..8037

MAPLE

sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if sd(n) = 10 then n else end if end proc: seq(a(n), n = 1 .. 800); # Emeric Deutsch, Jan 16 2009

MATHEMATICA

Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 7]], {s, Rest[IntegerPartitions[10]]}]]] (* T. D. Noe, Mar 08 2013 *)

Select[Range[1000], Total[IntegerDigits[#]] == 10 &] (* Vincenzo Librandi, Mar 10 2013 *)

PROG

(MAGMA) [n: n in [1..1000] | &+Intseq(n) eq 10 ]; // Vincenzo Librandi, Mar 10 2013

(Haskell)

a052224 n = a052224_list !! (n-1)

a052224_list = filter ((== 10) . a007953) [0..]

-- Reinhard Zumkeller, Jul 17 2014

(PARI) isok(n) = sumdigits(n) == 10; \\ Michel Marcus, Dec 28 2015

(PARI) \\ This algorithm needs a modified binomial.

C(n, k)=if(n>=k, binomial(n, k), 0)

\\ways to roll s-q with q dice having sides 0 through n - 1.

b(s, q, n)=if(s<=q*(n-1), s+=q; sum(i=0, q-1, (-1)^i*C(q, i)*C(s-1-n*i, q-1)), 0)

\\ main algorithm; this program applies to all sequences of the form "Numbers whose sum of digits is m."

a(n, {m=10}) = {my(q); q = 2; while(b(m, q, 10) < n, q++); q--; s = m; os = m; r=0; while(q, if(b(s, q, 10) < n, n-=b(s, q, 10); s--, r+=(os-s)*10^(q); os = s; q--)); r+= s; r}

\\ David A. Corneth, Jun 05 2016

CROSSREFS

Cf. A007953, A017173, A254524.

Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Cf. A242614, A242627.

Cf. A094677.

Cf. A018900, A187813.

Sum of base-b digits equal b: A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9).

Sequence in context: A065207 A084364 A094677 * A179955 A243994 A083678

Adjacent sequences:  A052221 A052222 A052223 * A052225 A052226 A052227

KEYWORD

nonn,base,easy

AUTHOR

Henry Bottomley, Feb 01 2000

EXTENSIONS

Incorrect formula deleted by N. J. A. Sloane, Jan 15 2009

Extended by Emeric Deutsch, Jan 16 2009

Offset changed by Bruno Berselli, Mar 07 2013

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 27 13:47 EDT 2017. Contains 284176 sequences.