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%I #44 Feb 09 2024 10:11:42
%S 49,58,67,76,85,94,139,148,157,166,175,184,193,229,238,247,256,265,
%T 274,283,292,319,328,337,346,355,364,373,382,391,409,418,427,436,445,
%U 454,463,472,481,490,508,517,526,535,544,553,562,571,580,607,616,625,634,643,652
%N Numbers with digitsum 13, in increasing order.
%C If 13 is considered as an 'unlucky' number: the 'unlucky years'.
%C A007953(a(n)) = 13; number of repdigits = A242627(13) = 1. - _Reinhard Zumkeller_, Jul 17 2014
%D The Guardian Weekly, July 25-31, 2008, p.39 puzzles 5., p31.
%H David A. Corneth, <a href="/A143164/b143164.txt">Table of n, a(n) for n = 1..10000</a>
%H Wolfdieter Lang, <a href="/A143164/a143164.txt">a(n) up to 3000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Triskaidekaphobia.html">Triskaidekaphobia</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Triskaidekaphobia">Triskaidekaphobia</a>
%F digitsum(a(n))=13, ordered increasingly.
%e 2029 is the next 'unlucky year'. Solution to the guardian weekly puzzle.
%e a(10^ 1) = 166
%e a(10^ 2) = 1309
%e a(10^ 3) = 21370
%e a(10^ 4) = 1100254
%e a(10^ 5) = 111032122
%e a(10^ 6) = 30611101000
%e a(10^ 7) = 40100300100301
%e a(10^ 8) = 200011001012211010
%e a(10^ 9) = 10001220000100012002100
%e a(10^10) = 1100000001010021010000000230 - _David A. Corneth_, Jan 31 2015
%t f[n_] := Rest@ Select[Range@ n, NestWhile[Plus @@ IntegerDigits[#] &, #, # > 14 &] == 13 &]; f@ 652 (* _Michael De Vlieger_, Feb 03 2015 *)
%t Select[Range[700],Total[IntegerDigits[#]]==13&] (* _Harvey P. Dale_, Oct 11 2017 *)
%o (Haskell)
%o a143164 n = a143164_list !! (n-1)
%o a143164_list = filter ((== 13) . a007953) [0..]
%o -- _Reinhard Zumkeller_, Jul 17 2014
%o (PARI)
%o \\This algorithm needs a modified binomial.
%o C(n,k)=if(n>=k,binomial(n,k),0)
%o \\ways to roll s-q with q dice having sides 0 through n - 1.
%o 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)
%o \\main algorithm
%o 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}
%o \\inverse
%o 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
%o (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
%o 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
%Y 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).
%Y Cf. A242614, A242627.
%K nonn,base,easy
%O 1,1
%A _Wolfdieter Lang_, Sep 15 2008
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