login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143164 Numbers with digitsum 13, in increasing order. 32
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

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

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: A162527 A028915 A090063 * A304950 A316618 A039472

Adjacent sequences:  A143161 A143162 A143163 * A143165 A143166 A143167

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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 08:48 EST 2018. Contains 317347 sequences. (Running on oeis4.)