A083825 -id:A083825 - 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

A083823 a(1) = 15; then numbers obtained at every stage of division by 3 in the following process: multiply by 3, reverse the digits, divide by 3, reverse the digits, multiply by 3, reverse the digit, divide by 3.

Original entry on oeis.org

15, 18, 114, 1107, 11004, 110007, 1100004, 11000007, 110000004, 1100000007, 11000000004, 110000000007, 1100000000004, 11000000000007, 110000000000004, 1100000000000007, 11000000000000004, 110000000000000007, 1100000000000000004, 11000000000000000007

Offset: 1

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

1. 15 is the smallest number which does not follow a cyclic pattern or terminates at k < 10. 2. A pattern is visible. For 12 one gets the cyclic pattern 12->36->63->21->12->36... for 14 one gets 14 ->42->24->8->8... Subsidiary sequences that could be considered: (1) Sequence of numbers which show cyclic pattern. (2) Sequence of numbers which terminate at k,k <10. (3) Numbers which gare not members of (1) and (2).

			*15->45->54->*18->81->243->342->*114->411->1233->3321->*1107->7011->21033->33012->*11004->
Numbers marked with * are members.

Cf. A083822, A083824, A083825.

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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A083823 a(1) = 15; then numbers obtained at every stage of division by 3 in the following process: multiply by 3, reverse the digits, divide by 3, reverse the digits, multiply by 3, reverse the digit, divide by 3.

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