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A143164
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Numbers with digitsum 13, in increasing order.
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32
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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The Guardian Weekly, July 25-31, 2008, p.39 puzzles 5., p31.
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LINKS
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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
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FORMULA
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digitsum(a(n))=13, ordered increasingly.
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EXAMPLE
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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
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MAPLE
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select(n->convert(convert(n, base, 10), `+`)=13, [$1..652]); # Paolo P. Lava, Jul 05 2019
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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: A162527 A028915 A090063 * A304950 A316618 A039472
Adjacent sequences: A143161 A143162 A143163 * A143165 A143166 A143167
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KEYWORD
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nonn,base,easy
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AUTHOR
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Wolfdieter Lang, Sep 15 2008
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STATUS
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approved
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