cp's OEIS Frontend

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

%I A367733 #54 Feb 02 2025 00:17:55
%S A367733 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,
%T A367733 29,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,51,52,53,54,
%U A367733 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
%N A367733 Numbers k such that the sum of digits of k is equal to the sum of digits of k+9.
%C A367733 Numbers k which end in the digits ...xy with x!=9 and y!=0.
%C A367733 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).
%C A367733 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.
%C A367733 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.
%H A367733 <a href="/index/Rec#order_82">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A367733 a(n) = n + floor((n-1)/9) + floor((n-1)/81)*10.
%e A367733 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.
%t A367733 Select[Range[100], Equal @@ Plus @@@ IntegerDigits[{#, # + 9}] &] (* _Amiram Eldar_, Nov 28 2023 *)
%o A367733 (Python)
%o A367733 def A367733(n): return n + (n-1)//9 + ((n-1)//81)*10
%o A367733 (PARI) is(n) = sumdigits(n) == sumdigits(n+9) \\ _David A. Corneth_, Nov 28 2023
%Y A367733 Cf. A007953.
%K A367733 nonn,easy,base
%O A367733 1,2
%A A367733 _Julia Zimmerman_, Nov 28 2023