Solution Found!
The Online Encyclopedia of Integer Sequences (OEIS) was
Chapter 3, Problem 88(choose chapter or problem)
The Online Encyclopedia of Integer Sequences (OEIS) was originated and maintained for many years by Neil Sloane, a mathematician at AT&T who has also written several books about sequences. The OEIS Foundation now manages the database, which contains more than 200,000 sequences of integers that have 180 Recursion, Recurrence Relations, and Analysis of Algorithms been submitted and studied by many people. (See oeis.org). There is even a YouTube movie about the OEIS! Recamans sequence (number A005132 in the OEIS catalog) is a recursive sequence defined as follows: a(1) = 1 For n > 1, a(n) = a(n 1) n if that number is positive and not already in the sequence, otherwise a(n 1) + n a. Confirm that the first few terms of this sequence are 1, 3, 6, 2, 7, 13. b. It has been conjectured that every nonnegative integer will eventually appear in this sequence. Find the index of this sequence at which the following numbers appear: 10, 12, 23.
Questions & Answers
QUESTION:
The Online Encyclopedia of Integer Sequences (OEIS) was originated and maintained for many years by Neil Sloane, a mathematician at AT&T who has also written several books about sequences. The OEIS Foundation now manages the database, which contains more than 200,000 sequences of integers that have 180 Recursion, Recurrence Relations, and Analysis of Algorithms been submitted and studied by many people. (See oeis.org). There is even a YouTube movie about the OEIS! Recamans sequence (number A005132 in the OEIS catalog) is a recursive sequence defined as follows: a(1) = 1 For n > 1, a(n) = a(n 1) n if that number is positive and not already in the sequence, otherwise a(n 1) + n a. Confirm that the first few terms of this sequence are 1, 3, 6, 2, 7, 13. b. It has been conjectured that every nonnegative integer will eventually appear in this sequence. Find the index of this sequence at which the following numbers appear: 10, 12, 23.
ANSWER:Step1 of 3
Recurrence relation:
The sequence in which next values are depends on the earlier value of the sequence is recurrence relation of that sequence.