A052222 -id:A052222 - cp's OEIS frontend

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

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

M. F. Hasler, Dec 23 2016

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

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).

Select[Range@ 240, Total@ IntegerDigits[6 #] == 12 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(6*n)==12
```

A268620 Numbers whose digital sum is a multiple of 4.

Original entry on oeis.org

0, 4, 8, 13, 17, 22, 26, 31, 35, 39, 40, 44, 48, 53, 57, 62, 66, 71, 75, 79, 80, 84, 88, 93, 97, 103, 107, 112, 116, 121, 125, 129, 130, 134, 138, 143, 147, 152, 156, 161, 165, 169, 170, 174, 178, 183, 187, 192, 196, 202, 206, 211, 215, 219, 220, 224, 228, 233, 237, 242, 246

Offset: 1

Bruno Berselli, Feb 09 2016

a(1498) = 5999 is the smallest term that is congruent to 5 modulo 9.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007953, A061383 (supersequence).
Cf. numbers whose digital sum is a multiple of k: A054683 (k=2), A008585 (k=3), this sequence (k=4), A227793 (k=5).
Subsequences: A002278, A038446, A052218, A052222, A061387, A169967, A235151, A235227, A235229.

[n: n in [0..250] | IsIntegral(&+Intseq(n)/4)];

select(t -> convert(convert(t,base,10),`+`) mod 4 = 0, [$1..1000]); # Robert Israel, Feb 09 2016

Select[Range[0, 250], IntegerQ[Total[IntegerDigits[#]]/4] &]

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

Eric Angelini, Aug 15 2024

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)

			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.

Michael S. Branicky, Table of n, a(n) for n = 1..6491

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).

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

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

M. F. Hasler, Dec 23 2016

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

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).

Select[Range@ 3664, Total@IntegerDigits[11 #] == 11 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(11*n)==11
```

cp's OEIS Frontend

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

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A268620 Numbers whose digital sum is a multiple of 4.

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

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

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Mathematica

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