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 A052224 Numbers whose sum of digits is 10. 52
 19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316, 325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 505, 514, 523, 532, 541, 550, 604, 613, 622, 631, 640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Proper subsequence of A017173. - Rick L. Shepherd, Jan 12 2009 Subsequence of A227793. - Michel Marcus, Sep 23 2013 A007953(a(n)) = 10; number of repdigits = #{55,22222,1^10} = A242627(10) = 3. - Reinhard Zumkeller, Jul 17 2014 a(n) = A094677(n) for n = 1..28. - Reinhard Zumkeller, Nov 08 2015 The number of terms having <= m digits is the coefficient of x^10 in sum(i=0,9,x^i)^m = ((1-x^10)/(1-x))^m. - David A. Corneth, Jun 04 2016 In general, the set of numbers with sum of base-b digits equal to b is a subset of { (b-1)*k + 1; k = 2, 3, 4, ... }. - M. F. Hasler, Dec 23 2016 LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 (first 3921 terms from T. D. Noe) FORMULA a(n+1) = A228915(a(n)) for any n > 0. - Rémy Sigrist, Jul 10 2018 MAPLE sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if sd(n) = 10 then n else end if end proc: seq(a(n), n = 1 .. 800); # Emeric Deutsch, Jan 16 2009 MATHEMATICA Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 7]], {s, Rest[IntegerPartitions[10]]}]]] (* T. D. Noe, Mar 08 2013 *) Select[Range[1000], Total[IntegerDigits[#]] == 10 &] (* Vincenzo Librandi, Mar 10 2013 *) PROG (Magma) [n: n in [1..1000] | &+Intseq(n) eq 10 ]; // Vincenzo Librandi, Mar 10 2013 (Haskell) a052224 n = a052224_list !! (n-1) a052224_list = filter ((== 10) . a007953) [0..] -- Reinhard Zumkeller, Jul 17 2014 (PARI) isok(n) = sumdigits(n) == 10; \\ Michel Marcus, Dec 28 2015 (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; this program applies to all sequences of the form "Numbers whose sum of digits is m." a(n, {m=10}) = {my(q); q = 2; while(b(m, q, 10) < n, q++); q--; s = m; os = m; 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} \\ David A. Corneth, Jun 05 2016 (Python) from sympy.utilities.iterables import multiset_permutations def auptodigs(maxdigits, b=10, sod=10): # works for any base, sum-of-digits alst = [sod] if 0 <= sod < b else [] nzdigs = [i for i in range(1, b) if i <= sod] nzmultiset = [] for d in range(1, b): nzmultiset += [d]*(sod//d) for d in range(2, maxdigits + 1): fullmultiset = [0]*(d-1-(sod-1)//(b-1)) + nzmultiset for firstdig in nzdigs: target_sum, restmultiset = sod - int(firstdig), fullmultiset[:] restmultiset.remove(firstdig) for p in multiset_permutations(restmultiset, d-1): if sum(p) == target_sum: alst.append(int("".join(map(str, [firstdig]+p)), b)) if p[0] == target_sum: break return alst print(auptodigs(4)) # Michael S. Branicky, Sep 14 2021 (Python) def A052224(N = 19): """Return a generator of the sequence of all integers >= N with the same digit sum as N.""" while True: yield N N = A228915(N) # skip to next larger integer with the same digit sum a = A052224(); [next(a) for _ in range(50)] # M. F. Hasler, Mar 16 2022 CROSSREFS Cf. A007953, A017173, A228915, A254524. Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20). Cf. A242614, A242627. Cf. A094677. Cf. A018900, A187813. Sum of base-b digits equal b: A226636 (b = 3), A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9). Sequence in context: A065207 A084364 A094677 * A179955 A243994 A083678 Adjacent sequences: A052221 A052222 A052223 * A052225 A052226 A052227 KEYWORD nonn,base,easy AUTHOR Henry Bottomley, Feb 01 2000 EXTENSIONS Incorrect formula deleted by N. J. A. Sloane, Jan 15 2009 Extended by Emeric Deutsch, Jan 16 2009 Offset changed by Bruno Berselli, Mar 07 2013 STATUS approved

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Last modified June 6 10:50 EDT 2023. Contains 363142 sequences. (Running on oeis4.)