A143164 Numbers with digitsum 13, in increasing order.

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

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

David A. Corneth, Table of n, a(n) for n = 1..10000

Wolfdieter Lang, a(n) up to 3000

Eric Weisstein's World of Mathematics, Triskaidekaphobia

Wikipedia, 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).

Cf. A242614, A242627.

Sequence in context: A028915 A345114 A090063 * A304950 A316618 A039472

Adjacent sequences: A143161 A143162 A143163 * A143165 A143166 A143167

Keyword

nonn,base,easy

Author

Wolfdieter Lang, Sep 15 2008

Status

approved