login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143164 Numbers with digitsum 13, in increasing order. 33
49, 58, 67, 76, 85, 94, 139, 148, 157, 166, 175, 184, 193, 229, 238, 247, 256, 265, 274, 283, 292, 319, 328, 337, 346, 355, 364, 373, 382, 391, 409, 418, 427, 436, 445, 454, 463, 472, 481, 490, 508, 517, 526, 535, 544, 553, 562, 571, 580, 607, 616, 625, 634, 643, 652 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If 13 is considered as an 'unlucky' number: the 'unlucky years'.
A007953(a(n)) = 13; number of repdigits = A242627(13) = 1. - Reinhard Zumkeller, Jul 17 2014
REFERENCES
The Guardian Weekly, July 25-31, 2008, p.39 puzzles 5., p31.
LINKS
Wolfdieter Lang, a(n) up to 3000
Eric Weisstein's World of Mathematics, Triskaidekaphobia
FORMULA
digitsum(a(n))=13, ordered increasingly.
EXAMPLE
2029 is the next 'unlucky year'. Solution to the guardian weekly puzzle.
a(10^ 1) = 166
a(10^ 2) = 1309
a(10^ 3) = 21370
a(10^ 4) = 1100254
a(10^ 5) = 111032122
a(10^ 6) = 30611101000
a(10^ 7) = 40100300100301
a(10^ 8) = 200011001012211010
a(10^ 9) = 10001220000100012002100
a(10^10) = 1100000001010021010000000230 - David A. Corneth, Jan 31 2015
MATHEMATICA
f[n_] := Rest@ Select[Range@ n, NestWhile[Plus @@ IntegerDigits[#] &, #, # > 14 &] == 13 &]; f@ 652 (* Michael De Vlieger, Feb 03 2015 *)
Select[Range[700], Total[IntegerDigits[#]]==13&] (* Harvey P. Dale, Oct 11 2017 *)
PROG
(Haskell)
a143164 n = a143164_list !! (n-1)
a143164_list = filter ((== 13) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014
(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
a(n) = {my(q); q = 2; while(b(13, q, 10) < n, q++); q--; s = 13; os = 13; 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}
\\inverse
inv(n)={r = 1; v=digits(n); l=v[#v]; forstep(i = #v-1, 1, -1, for(j=1, v[i], r+=b(l+j, #v-i, 10)); l+=v[i]); r} \\ David A. Corneth, Jan 31 2015
(PARI) transform(n, b)=my(d=digits(n), nd=#d, v=vector(b, i, [i\10, b-(b+1-i)\10]), k); v[b][2]=d[1]; v
list(lim)=my(v=List(), d=transform(lim\=1, 13)); forvec(u=transform(lim\1, 13), if(u[4]<u[10] || (u[1]<u[10] && u[2]<u[11] && u[3]<u[12] && u[4]<u[13]), my(s=sum(i=1, 13, 10^u[i])); if(s<=lim, listput(v, s))), 1); Set(v) \\ Charles R Greathouse IV, May 30 2019
CROSSREFS
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Sequence in context: A028915 A345114 A090063 * A304950 A316618 A039472
KEYWORD
nonn,base,easy
AUTHOR
Wolfdieter Lang, Sep 15 2008
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)