A193239 -id:A193239 - cp's OEIS frontend

A193306 Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the reversed number from original.

0, 1, 2, 1, 4, 1, 4, 1, 4, 1, 4, 3, -1, -1, 4, 1, -1, 1, 4, -1, -1, 1, 4, -1, 2, 11, -1, 1, 2, 11, -1, 1, -1, 1, 12, 11, -1, 3, 2, -1, 6, -1, -1, -1, -1, 1, 12, 11, 4, -1, -1, 1, 8, 5, -1, 3, -1, 3, 6, -1, 4, -1, -1, 1, 2, 1, 2, -1, -1, -1, -1, 3, 2, 1, 2

Offset: 0

Kerry Mitchell, Jul 22 2011

			Decimal 2 is 10 in binary, which is -1+i using complex base -1+i. Reversing 10 gives 01, or 1+0i.  Subtracting the reversed from the original results in -2+i, or 11111 using the complex base.  Its reversal is the same, so subtracting them gives 0.  Decimal 2 took 2 steps to reach 0, so a(2) = 2.

Kerry Mitchell, Table of n, a(n) for n = 0..10000
W. J. Gilbert, Arithmetic in Complex Bases, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.

Cf A193239, number of steps needed to reach a palindrome with complex base -1+i. A193307, Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the original number from the reversed.

A193240 Trajectory of binary number 110 (decimal 6) under the operation "Reverse and Add" carried out with complex base -1+i.

Original entry on oeis.org

110, 11101, 10110, 11101011, 1110100111000, 1110001101111, 1100100110101100, 1110011000111111, 1100110101111011100, 1000110010101111, 1111101001000000010

Offset: 0

Kerry Mitchell, Jul 19 2011

			The initial term is 110. Using complex base -1+i, this is -1-i. Reversing 110 gives 011, which is 0+i.  Adding both terms gives -1+0i, which is 11101, the second term.

Kerry Mitchell, Table of n, a(n) for n = 0..500
W. J. Gilbert, Arithmetic in Complex Bases, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.

Cf A193239, number of steps needed to reach a palindrome with complex base -1+i. For that sequence, a(6)=-1, showing that decimal 6 (binary 110) seems to not reach a palindrome under the "Reverse and Add" iteration. Cf A193241, the trajectory of 10100 (decimal 20).

A193241 Trajectory of binary number 10100 (decimal 20) under the operation "Reverse and Add" carried out with complex base -1+i.

Original entry on oeis.org

10100, 11100001, 11111011010, 1111110111101, 1111101110011110, 111010001110001001, 110011110000010000010, 10100101110110101001, 1110100101000001111001010000, 111010111010100100100000111, 111101010011100000011010100

Offset: 0

Kerry Mitchell, Jul 19 2011

			The initial term is 10100. Using complex base -1+i, this is -4-2i. Reversing 10100 gives 00101, which is 1-2i.  Adding both terms gives -3-4i, which is 11100001, the second term.

Kerry Mitchell, Table of n, a(n) for n = 0..500
W. J. Gilbert, Arithmetic in Complex Bases, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.

Cf A193239, number of steps needed to reach a palindrome with complex base -1+i. For that sequence, a(20)=-1, showing that decimal 20 (binary 10100) seems to not reach a palindrome under the "Reverse and Add" iteration. Cf A193240, the trajectory of 110 (decimal 6) under the "Reverse and Add" iteration with complex base -1+i.

A193307 Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the original number from the reversed.

Original entry on oeis.org

0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 2, 15, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 3, -1, 1, -1, 3, -1, 1, -1, 1, -1, 3, 2, -1, -1, 15, -1, -1, -1, -1, -1, 1, -1, 3, -1, -1, -1, 1, -1, 7, 2, -1, 2, -1, -1, -1, -1, -1, -1, 1, 14, 1, -1, -1, 6, -1, -1

Offset: 0

Kerry Mitchell, Jul 22 2011

			Decimal 12 is 1100 in binary, which is 2+0i using complex base -1+i. Reversing 1100 gives 0011, or 0+i. Subtracting the original number from the reversed results in -2+i, or 11111 using the complex base. Its reversal is the same, so subtracting them gives 0. Decimal 12 took 2 steps to reach 0, so a(12) = 2.

Kerry Mitchell, Table of n, a(n) for n = 0..10000
W. J. Gilbert, Arithmetic in Complex Bases, Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 77-81.

Cf. A193239 (number of steps needed to reach a palindrome with complex base -1+i).

Cf. A193306 (number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the reversed number from the original).

cp's OEIS Frontend

A193306 Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the reversed number from original.

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A193240 Trajectory of binary number 110 (decimal 6) under the operation "Reverse and Add" carried out with complex base -1+i.

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A193241 Trajectory of binary number 10100 (decimal 20) under the operation "Reverse and Add" carried out with complex base -1+i.

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A193307 Number of 'Reverse and Subtract' steps needed to reach 0, or -1 if never reaches 0, using base -1+i and subtracting the original number from the reversed.

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