A053840 -id:A053840 - cp's OEIS frontend

A053837 Sum of digits of n modulo 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5

Offset: 0

Henry Bottomley, Mar 28 2000

			a(59)=4 because 5+9 = 14 = 4 mod 10.

Cf. A007953, A010879.

Cf. A000120, A010060, A053838, A053839, A053840, A053841, A053842, A053843, A053844.

Table[Mod[Total[IntegerDigits[n]],10],{n,0,120}] (* Harvey P. Dale, Oct 02 2018 *)

a(n)=sumdigits(n)%10 \\ Charles R Greathouse IV, Feb 02 2023

a(n) = A010879(A007953(n)) = (n+a(floor[n/10])) mod 10. So can construct sequence by starting with 0 and mapping 0->0123456789, 1->1234567890, 2->2345678901 etc. (e.g. 0, 0123456789, 0123456789123456789023456789013456789012456..., etc.) and looking at n-th digit of a term with sufficient digits.

A079498 Numbers whose sum of digits in base b gives 0 (mod b), for b = 3.

Original entry on oeis.org

0, 5, 7, 11, 13, 15, 19, 21, 26, 29, 31, 33, 37, 39, 44, 45, 50, 52, 55, 57, 62, 63, 68, 70, 74, 76, 78, 83, 85, 87, 91, 93, 98, 99, 104, 106, 109, 111, 116, 117, 122, 124, 128, 130, 132, 135, 140, 142, 146, 148, 150, 154, 156, 161, 163, 165, 170, 171, 176, 178, 182, 184

Offset: 1

Carlos Alves, Jan 21 2003

In base 2 this gives the "Evil Numbers" (cf. A001969). One may conjecture that in base b the asymptotic slope will be b and asymptotic density 1/b for each result (mod b). Cases b=31 or b=61 gave considerable number of primes on the sequence.
Proof of this conjecture: in general, the sequence d with terms d(n) = sum of digits of n written in base b (mod b) is a fixed point of the generalized Thue-Morse morphism 0->01..b-1, 1->12..0, etc. See A053839 for the case b=4. It follows directly from this that all symbols have asymptotic density 1/b, and therefore that the positional sequences all have asymptotic slope b. - Michel Dekking, Apr 18 2019
Positions of 0's in A053838. Cf. A026601.

			83 is a term since 83 = (1,0,0,0,2)_3 and 1 + 0 + 0 + 0 + 2 = 3 == 0 (mod 3).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001969. See A053840 for base b=5. See A141803 for an array with all b.

Ev = Function[{b, x}, vx = IntegerDigits[x, b]; Mod[Apply[Plus, vx], b]]; Seq = Function[{b, n}, Flatten[Position[Table[Ev[b, k], {k, 0, n}], 0]] - 1]; sb = Seq[3, 1000]

a(1) = 0 inserted and offset corrected by Amiram Eldar, Jan 05 2020

cp's OEIS Frontend

A053837 Sum of digits of n modulo 10.

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