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

Author

Wolfdieter Lang, Sep 15 2008

Keywords

• nonn
• base
• easy

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

Examples

			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
		

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

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.

Programs

Haskell

a143164 n = a143164_list !! (n-1)
a143164_list = filter ((== 13) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

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 *)

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]Charles R Greathouse IV, May 30 2019

Formula

digitsum(a(n))=13, ordered increasingly.