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 A226636 Numbers whose base-3 sum of digits is 3. 11
 5, 7, 11, 13, 15, 19, 21, 29, 31, 33, 37, 39, 45, 55, 57, 63, 83, 85, 87, 91, 93, 99, 109, 111, 117, 135, 163, 165, 171, 189, 245, 247, 249, 253, 255, 261, 271, 273, 279, 297, 325, 327, 333, 351, 405, 487, 489, 495, 513, 567, 731, 733, 735, 739, 741, 747, 757 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All of the entries are odd. Subsequence of A005408. - Michel Marcus, Sep 03 2013 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 Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(k^3/6 + k^2 + 5*k/6 + j) = 3^(k+1) + A055235(j-1) for 1 <= j <= k^2/2+5*k/2+2. - Robert Israel, Jun 05 2018 EXAMPLE The ternary expansion of 5 is (1,2), which has sum of digits 3. The ternary expansion of 31 is (1,0,0,2), which has sum of digits 3. 10 is not on the list since the ternary expansion of 10 is (1,0,1), which has sum of digits 2 not 3. MAPLE N:= 10: # for all terms < 3^(N+1) [seq(seq(seq(3^a+3^b+3^c, c=0..`if`(b=a, b-1, b)), b = 0..a), a=0..N)]; # Robert Israel, Jun 05 2018 MATHEMATICA Select[Range@ 757, Total@ IntegerDigits[#, 3] == 3 &] (* Michael De Vlieger, Dec 23 2016 *) PROG (Sage) [i for i in [0..1000] if sum(Integer(i).digits(base=3))==3] (PARI) select( is(n)=sumdigits(n, 3)==3, [1..999]) \\ M. F. Hasler, Dec 23 2016 (Python) from itertools import islice def nextsod(n, base): c, b, w = 0, base, 0 while True: d = n%b if d+1 < b and c: return (n+1)*b**w + ((c-1)%(b-1)+1)*b**((c-1)//(b-1))-1 c += d; n //= b; w += 1 def A226636gen(sod=3, base=3): # generator of terms for any sod, base an = (sod%(base-1)+1)*base**(sod//(base-1))-1 while True: yield an; an = nextsod(an, base) print(list(islice(A226636gen(), 57))) # Michael S. Branicky, Jul 10 2022, generalizing the code by M. F. Hasler in A052224 CROSSREFS Cf. A018900, A023694, A055235, A187813. Cf. A226969 (b = 4), A227062 (b = 5), A227080 (b = 6), A227092 (b = 7), A227095 (b = 8), A227238 (b = 9), A052224 (b = 10). Sequence in context: A280199 A196276 A079498 * A287517 A175100 A270998 Adjacent sequences: A226633 A226634 A226635 * A226637 A226638 A226639 KEYWORD nonn,base AUTHOR Tom Edgar, Aug 31 2013 STATUS approved

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Last modified December 10 19:44 EST 2023. Contains 367717 sequences. (Running on oeis4.)