A367733 Numbers k such that the sum of digits of k is equal to the sum of digits of k+9.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 101

Offset: 1

Author

Julia Zimmerman, Nov 28 2023

Keywords

• nonn
• easy
• base

Comments

Numbers k which end in the digits ...xy with x!=9 and y!=0.

Differs from A052382, as there are terms with 0 here, the first being a(82)=101. First differs from A067251 at a(82)=101, A067251(82)=91. Similarly to A067251, A209931 includes 91-99 as terms whereas they are not in this sequence. A043095(1)=0 and A023804(1)=0 whereas 0 is not a term in this sequence (there are additional differences, such as the term that comes after 89 in A023804 and A043095 being 99).

This sequence is defined as follows: |digsum(k + seed) - digsum(k)| = r where digsum is the digital sum (A007953), with seed = 9 and r = 0.

The way this sequence looks has to do with using base 10: if you choose 8 as a seed and 1 as the sought difference (r), or 7 as a seed and 2 as the sought difference, you will get similar long, full sequences. However if you choose 8 as a seed and 0 as the sought difference, you'll get no terms.

Examples

			For k=3, 3 + 9 = 12. Sum of 1 + 2 = 3. Since the sum of the digits in 3 and the sum of the digits in 12 are the same, 3 is a term of the sequence.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A007953.

Programs

Mathematica

Select[Range[100], Equal @@ Plus @@@ IntegerDigits[{#, # + 9}] &] (* Amiram Eldar, Nov 28 2023 *)

PARI

is(n) = sumdigits(n) == sumdigits(n+9) \\ David A. Corneth, Nov 28 2023

Python

def A367733(n): return n + (n-1)//9 + ((n-1)//81)*10

Formula

a(n) = n + floor((n-1)/9) + floor((n-1)/81)*10.