A384276 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number that is coprime to a(n-1) while the total number of prime factors, counted with multiplicity, of the form 4*k+1 and 4*k+3 for all terms a(1)..a(n) never differs by more than 1.
1, 2, 3, 4, 5, 6, 13, 7, 8, 15, 16, 17, 10, 9, 20, 11, 25, 12, 19, 26, 23, 29, 14, 37, 22, 35, 32, 39, 34, 31, 30, 41, 24, 53, 28, 51, 40, 43, 50, 21, 52, 45, 58, 47, 55, 61, 38, 65, 18, 73, 44, 75, 46, 85, 33, 64, 87, 68, 59, 60, 89, 48, 91, 74, 67, 70
Offset: 1
Keywords
Examples
a(6) = 6 as in a(1)..a(5) the total number of prime factors of the form 4*k+1 is one (5) while the total number of prime factors of the form 4*k+3 is one (3). As 6 only contains one prime factor of either form, and is coprime to 5, it can be chosen. a(7) = 13 as in a(1)..a(6) the total number of prime factors of the form 4*k+1 is one (5) while the total number of prime factors of the form 4*k+3 is two (3,6). Therefore a(7) must contain between zero and two more prime factors of the form 4*k+1 than those of the form 4*k+3 while being coprime to 6. The smallest unused number meeting both of those conditions is 13.
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..10000
- Scott R. Shannon, Image of the first 10000 terms. The colors are graduated across the spectrum to show the total number of prime factors of each term, with red being one prime factor. The green line is a(n) = n.
- Wikipedia, Chebyshev's bias.
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