cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 31-34 of 34 results.

A279776 Numbers n such that the sum of digits of 6n equals 12.

Original entry on oeis.org

8, 11, 14, 23, 26, 29, 32, 38, 41, 44, 47, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 86, 89, 92, 95, 101, 104, 107, 110, 119, 122, 125, 134, 137, 140, 152, 155, 173, 176, 179, 182, 188, 191, 194, 197, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 236
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088408 = A062768/6 and A279769 (the analog for 9).

Crossrefs

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Programs

  • Mathematica
    Select[Range@ 240, Total@ IntegerDigits[6 #] == 12 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    is(n)=sumdigits(6*n)==12

A227793 Numbers whose digital sum is a multiple of 5.

Original entry on oeis.org

0, 5, 14, 19, 23, 28, 32, 37, 41, 46, 50, 55, 64, 69, 73, 78, 82, 87, 91, 96, 104, 109, 113, 118, 122, 127, 131, 136, 140, 145, 154, 159, 163, 168, 172, 177, 181, 186, 190, 195, 203, 208, 212, 217, 221, 226, 230, 235, 244, 249, 253, 258, 262, 267, 271, 276
Offset: 1

Views

Author

Michel Marcus, Sep 23 2013

Keywords

Comments

Most first differences are 5, 9 and 4. First differences are strictly less than 10. First occurrences d of first difference a(i+1) - a(i) are for (d, i, a(i)) in {(5,1,0), (9,2,5), (4,4,19), (8,20,96), (3,60,299), (7,100, 997), (2,800,3999), (6, 2000, 9998), (1,10000,49999)}. - William Hitt, Apr 21 2014; comments modified by David A. Corneth, Jun 08 2016
a(10000) = 49999 is the smallest term that is congruent to 4 modulo 9. - Bruno Berselli, Feb 09 2016

Crossrefs

Cf. A007953.
Subsequences: A052219, A052224.

Programs

  • Magma
    [n: n in [0..300] | IsZero(&+Intseq(n) mod 5)]; // Bruno Berselli, Sep 23 2013
  • Magma
    [n: n in [0..300] | IsIntegral(&+Intseq(n)/5)];  // Bruno Berselli, Feb 09 2016
  • Mathematica
    Select[Range[0, 280], IntegerQ[Total[IntegerDigits[#]]/5] &] (* Bruno Berselli, Feb 09 2016 *)
  • PARI
    isok(n) = {if (n == 0, return (1)); digs = digits(n); return (sum(i=1, #digs, digs[i]) % 5 == 0);} \\ Michel Marcus, Sep 23 2013
  • PARI
    a(n) = n--;m=10*(n\2);s=sumdigits(m);m+(4-(s-1)%5)+5*(n%2==1) \\ David A. Corneth, Jun 05 2016

A375460 Lexicographically earliest sequence of distinct nonnegative terms arranged in successive chunks whose digitsum = 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 10, 11, 20, 6, 12, 100, 7, 21, 8, 101, 9, 1000, 13, 14, 10000, 15, 22, 16, 30, 17, 110, 18, 100000, 19, 23, 31, 1000000, 24, 40, 25, 102, 26, 200, 27, 10000000, 28, 32, 41, 33, 103, 34, 111, 35, 1001, 36, 100000000, 37, 42, 112, 43, 120, 44, 1010, 45, 1000000000
Offset: 1

Views

Author

Eric Angelini, Aug 15 2024

Keywords

Comments

The first integer that will never appear in the sequence is 29, as its digitsum exceeds 10.
From Michael S. Branicky, Aug 16 2024: (Start)
Infinite since A052224 is infinite (as are all sequences with digital sum 1..10).
a(6492) has 1001 digits. (End)

Examples

			The first chunk of integers with digitsum 10 is (0,1,2,3,4);
the next one is (5,10,11,20),
the next one is (6,12,100),
the next one is (7,21),
the next one is (8,101),
the next one is (9,1000),
the next one is (13,14,10000), etc.
The concatenation of the above chunks produce the sequence.

Links

Crossrefs

Cf. A166311, A051885, A228915.
Numbers with digital sum 1..10: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10).

Programs

  • Python
    from itertools import islice
def bgen(ds): # generator of terms with digital sum ds
    def A051885(n): return ((n%9)+1)*10**(n//9)-1 # due to Chai Wah Wu
    def A228915(n): # due to M. F. Hasler
        p = r = 0
        while True:
            d = n % 10
            if d < 9 and r: return (n+1)*10**p + A051885(r-1)
            n //= 10; r += d; p += 1
    k = A051885(ds)
    while True: yield k; k = A228915(k)
def agen(): # generator of terms
    an, ds_block = 0, 0
    dsg = [None] + [bgen(i) for i in range(1, 11)]
    dsi = [None] + [(next(dsg[i]), i) for i in range(1, 11)]
    while True:
        yield an
        an, ds_an = min(dsi[j] for j in range(1, 11-ds_block))
        ds_block = (ds_block + ds_an)%10
        dsi[ds_an] = (next(dsg[ds_an]), ds_an)
print(list(islice(agen(), 61))) # Michael S. Branicky, Aug 16 2024

Extensions

a(46) and beyond from Michael S. Branicky, Aug 16 2024.

A279771 Numbers n such that the sum of digits of 11n equals 11.

Original entry on oeis.org

19, 28, 37, 46, 55, 64, 73, 82, 190, 280, 370, 460, 550, 640, 730, 820, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1819, 1828, 1837, 1846, 1855, 1864, 1873, 1882, 1891, 1900, 2728, 2737, 2746, 2755, 2764, 2773, 2782, 2791, 2800, 3637, 3646, 3655, 3664
Offset: 1

Views

Author

M. F. Hasler, Dec 23 2016

Keywords

Comments

Inspired by A088404 = A069537/2 through A088410 = A069543/8.

Crossrefs

Cf. A007953 (digital sum), Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).

Programs

  • Mathematica
    Select[Range@ 3664, Total@IntegerDigits[11 #] == 11 &] (* Michael De Vlieger, Dec 23 2016 *)
  • PARI
    is(n)=sumdigits(11*n)==11
Previous Showing 31-34 of 34 results.

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