A265326 -id:A265326 - cp's OEIS frontend

A056965 a(n) = n - (reversal of digits of n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, -9, -18, -27, -36, -45, -54, -63, -72, 18, 9, 0, -9, -18, -27, -36, -45, -54, -63, 27, 18, 9, 0, -9, -18, -27, -36, -45, -54, 36, 27, 18, 9, 0, -9, -18, -27, -36, -45, 45, 36, 27, 18, 9, 0, -9, -18, -27, -36, 54, 45, 36, 27, 18, 9, 0, -9, -18, -27, 63, 54, 45, 36, 27, 18, 9, 0, -9, -18, 72, 63, 54

Offset: 0

Henry Bottomley, Jul 18 2000

a(n) is a multiple of 9.

			a(17) = 17 - 71 = -54.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for the Kaprekar map

Cf. A004086, A056964, A068396, A151949, A265326.

a056965 n = n - a004086 n  -- Reinhard Zumkeller, Sep 17 2013

a:= n-> (s-> n-parse(cat(s[-i]$i=1..length(s))))(""||n):
seq(a(n), n=0..82);  # Alois P. Heinz, Jul 11 2021

Table[n - FromDigits[Reverse[IntegerDigits[n]]], {n, 0, 82}] (* Jayanta Basu, Jul 11 2013 *)

a(n) = n - fromdigits(Vecrev(digits(n))); \\ Michel Marcus, Dec 20 2023

def a(n): return n - int(str(n)[::-1]) # Osman Mustafa Quddusi, Jul 11 2021

a(n) = n - A004086(n) = 2*n - A056964(n).

A055945 a(n) = n - (reversal of base-2 digits of n) (and then the result is written in base 10).

Original entry on oeis.org

0, 0, 1, 0, 3, 0, 3, 0, 7, 0, 5, -2, 9, 2, 7, 0, 15, 0, 9, -6, 15, 0, 9, -6, 21, 6, 15, 0, 21, 6, 15, 0, 31, 0, 17, -14, 27, -4, 13, -18, 35, 4, 21, -10, 31, 0, 17, -14, 45, 14, 31, 0, 41, 10, 27, -4, 49, 18, 35, 4, 45, 14, 31, 0, 63, 0, 33, -30, 51, -12, 21, -42, 63, 0, 33, -30, 51, -12, 21, -42, 75, 12, 45, -18, 63, 0, 33, -30, 75, 12, 45

Offset: 0

Henry Bottomley, Jul 18 2000

a(n) is even if n is odd and a(n) is odd if n is even; this is caused by the kind of swapping the most significant and least significant binary digit when reversing n and the fact that the most significant digit of n is always 1. - R. J. Mathar, Nov 05 2015

Alois P. Heinz, Table of n, a(n) for n = 0..16384
Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of n mod 8)

Cf. A030101, A030109, A265326.

a:= proc(n) local m, r; m:=n; r:=0;
      while m>0 do r:= r*2 +irem(m, 2, 'm') od;
      n-r
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 02 2015

Array[# - IntegerReverse[#, 2] &, 90, 0] (* Michael De Vlieger, Sep 06 2019 *)

For 2^m <= n <= 2^(m+1), we have n - 2^(m+1) <= a(n) <= n. - N. J. A. Sloane, May 29 2016

a(n) = n - A030101(n).

A309574 n-th prime minus its ternary (base 3) reversal.

Original entry on oeis.org

0, 2, -2, 2, -8, 0, -8, 8, 0, -26, -6, 6, -26, -6, -14, -26, -6, 14, 26, -6, 38, 26, -80, -128, -48, -80, -24, -128, 24, -80, 24, -80, -32, 24, -56, 0, 24, 80, -24, 0, -48, 80, 24, 80, -24, 104, 80, 80, 48, 104, 0, 24, 80, -398, -338, -278, -434, 18, -138

Offset: 1

Samuel M. A. Luque Astorga, Aug 08 2019

a(n) = 0 if and only if n is palindromic in base 3 - if and only if A000040(n) is in A014190.
As it occurs in its binary cousin, we observe that a scatter plot of this sequence shows parallelograms.
All terms are even. - Alois P. Heinz, Aug 08 2019

Robert Israel, Table of n, a(n) for n = 1..10000
Samuel M. A. Luque, C++ Program (.cpp file) to generate this sequence in whichever m-th base you choose.
Samuel M. A. Luque, Scatter plot of a(n) up to n = 8132 (primes up to 50 000).

Cf. A000040, A014190, A030102, A055947, A265326.

a:= n-> (p-> p-(l->add(l[-i]*3^(i-1), i=1..nops(l))
        )(convert(p, base, 3)))(ithprime(n)):
seq(a(n), n=1..61);  # Alois P. Heinz, Aug 08 2019

(# - IntegerReverse[#,3]) &@ Prime@ Range@ 60 (* Giovanni Resta, Aug 09 2019 *)

a(n) = my(p=prime(n)); p - fromdigits(Vecrev(digits(p, 3)), 3); \\ Michel Marcus, Aug 09 2019

from sympy import primerange
def rev(n, b):
    m = 0
    while n > 0:
        m, n = m*b+n%b, n//b
    return m
n, aa = 1, 1
while n <20:
    if aa in primerange(1,200):
        print(n, aa-rev(aa, 3))
        n = n+1
    aa = aa+1 # A.H.M. Smeets, Aug 09 2019

a(n) = A000040(n) - A030102(A000040(n)).

a(n) = A055947(A000040(n)).

cp's OEIS Frontend

A056965 a(n) = n - (reversal of digits of n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula

A055945 a(n) = n - (reversal of base-2 digits of n) (and then the result is written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A309574 n-th prime minus its ternary (base 3) reversal.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula