A083823 -id:A083823 - cp's OEIS frontend

A083822 a(n) = digit reversal of 3*n, divided by 3.

1, 2, 3, 7, 17, 27, 4, 14, 24, 1, 11, 21, 31, 8, 18, 28, 5, 15, 25, 2, 12, 22, 32, 9, 19, 29, 6, 16, 26, 3, 13, 23, 33, 67, 167, 267, 37, 137, 237, 7, 107, 207, 307, 77, 177, 277, 47, 147, 247, 17, 117, 217, 317, 87, 187, 287, 57, 157, 257, 27, 127, 227, 327, 97, 197, 297, 34

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

If n is a multiple of 10, then a(n) = a(n/10); if n is not a multiple of 10, then a(a(n)) = n.

			a(25) = reverse(3*25)/3 = reverse(75)/3 = 57/3 = 19.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A083823, A083824, A083825.

Table[FromDigits[Reverse[IntegerDigits[3n]]]/3,{n,70}] (* Harvey P. Dale, May 19 2015 *)
IntegerReverse[3*Range[70]]/3 (* Harvey P. Dale, Apr 12 2022 *)

{for(n=1,70,k=3*n; rev=0; while(k>0,d=divrem(k,10); k=d[1]; rev=10*rev+d[2]); print1(rev/3,","))}

apply( A083822(n)=fromdigits(Vecrev(digits(3*n)))/3, [0..99]) \\ M. F. Hasler, May 21 2021

Edited, corrected and extended by Klaus Brockhaus, May 11 2003

A083824 a(n) = digit reversal of 9*n, divided by 9.

Original entry on oeis.org

0, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 89, 79, 69, 59, 49, 39, 29, 19, 9, 109, 99, 78, 68, 58, 48, 38, 28, 18, 8, 108, 98, 88, 67, 57, 47, 37, 27, 17, 7, 107, 97, 87, 77, 56, 46, 36, 26, 16, 6, 106, 96, 86, 76, 66, 45, 35, 25, 15, 5, 105, 95, 85, 75, 65, 55, 34, 24, 14, 4, 104, 94, 84

Offset: 0

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

If n is a multiple of 10, then a(n) = a(n/10); if n is not a multiple of 10, then a(a(n)) = n.

			a(2) = reverse(9*2)/9 = reverse(18)/9 = 81/9 = 9.

Cf. A083822 (analog for 3), A083823, A083825.

{for(n=0,73,k=9*n; rev=0; while(k>0,d=divrem(k,10); k=d[1]; rev=10*rev+d[2]); print1(rev/9,","))}

apply( {A083824(n)=fromdigits(Vecrev(digits(9*n)))/9}, [0..99]) \\ M. F. Hasler, May 21 2021

Edited, corrected and extended by Klaus Brockhaus, May 11 2003

Minor edits and extension to offset 0 by M. F. Hasler, May 21 2021

A083825 a(1) = 12; then numbers obtained at every stage of division by 9 in the following process. multiply by 9, reverse the digits, divide by 9, reverse the digits, multiply by 9, reverse the digit, divide by 9, ...

Original entry on oeis.org

12, 89, 32, 78, 43, 67, 54, 56, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 09 2003

The interesting pattern of terminating at 65 after which every term is 65 is visible. 89 onwards alternate terms are obtained by subtracting 11 and 32 onwards alternate terms are obtained by adding 11 and both terminate at 65. Conjecture: Every such sequence for an n-digit number not divisible by 10 terminates in another n-digit number. Let it be t(n), then one also gets t(10k) =t(k). E.g. t(12) = 65. Subsidiary sequence:(1) a(n) = t(n), a(10k) = a(k). (2). The index of the first occurrence of t(n). A measure of the length of the cycle.

			*12--->108--->801--->*89--->98--->882---288-->*32--->23--->207--->702--->*78--->87--->783--->387--->*43--->34--->306--->603--->*67--->76...

Cf. A083822, A083823, A083824.

cp's OEIS Frontend

A083822 a(n) = digit reversal of 3*n, divided by 3.

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A083824 a(n) = digit reversal of 9*n, divided by 9.

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A083825 a(1) = 12; then numbers obtained at every stage of division by 9 in the following process. multiply by 9, reverse the digits, divide by 9, reverse the digits, multiply by 9, reverse the digit, divide by 9, ...

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