OFFSET
1,2
COMMENTS
The majority of terms are concentrated along two lines, the upper line has gradient of approximately 1.37 while the lower line has a gradient of approximately 1.02. Between these a third more random line also appear. See the linked image.
Small numbers with only 2 and 3 as prime divisors apparently take many terms to appear. For example a(210613) = 6, a(224221) = 18, while 12 and 24 have not appeared after 250000 terms.
LINKS
Scott R. Shannon, Image of the first 250000 terms.
EXAMPLE
a(3) = 3 as the divisors of 3 are 1 and 3, and a(3-1) = a(2) = 2, a(3+1) = a(4) = 5, and a(3+3) = a(6) = 7, and the gcd of 3 and each of these three numbers is 1. As a(3-3) = a(0) is not defined this term is ignored.
a(11) = 10 as the divisors of 10 are 1, 2, 5 and 10, and a(11-1) = a(10) = 13, a(11-2) = a(9) = 11, a(11-5) = a(6) = 7, a(11-10) = a(1) = 1, a(11+1) = a(12) = 17, a(11+2) = a(13) = 19, a(11+5) = a(16) = 23, and a(11+10) = a(21) = 27, and the gcd of 10 and each of these eight numbers is 1.
a(13) = 19 as the divisors of 19 are 1 and 19, and a(13-1) = a(12) = 17, a(13+1) = a(14) = 14, and a(13+19) = a(32) = 34, and the gcd of 19 and each of these three numbers is 1. Note that as a(11) = 10, and a(11+2) = a(13), where 2 is a divisor of 10, a(13) cannot equal 15 as gcd(10,15) > 1. This is the first term that differs from A347179.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Scott R. Shannon, Aug 30 2021
STATUS
approved