OFFSET
1,2
COMMENTS
See the assembly [a(n),a(n+1)] as a decimal number. Round this number to the closest integer. All rounded assemblies will produce a prime number.
"Rounding to the closest integer" is ambiguous for decimal numbers like (k.5) where k is an integer. Here we round such numbers to be rounded to k+1. The only occurrence of such a "rounding ambiguity" in the sequence happens with a(1) = 1 and a(2) = 5. Indeed, no more (k.5) "dilemmas" like that one will ever occur again as the integers 50, 500, 5000,... (that might produce together with the previous term k the decimal number k.50 or k.500 or k.5000...) cannot be part of the sequence; this is because 50, 500, 5000,... are not primes themselves (they end with 0) and neither are 51, 501, 5001,... (they are divisible by 3).
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..5001
EXAMPLE
The sequence starts with 1,5,2,3,4,6,7,10,52,53,11,12,58,59,13,...
The assembly [a(1),a(2)] is 1.5 which rounded upwards produces 2;
The assembly [a(2),a(3)] is 5.2 which rounded to the closest integer produces 5;
The assembly [a(3),a(4)] is 2.3 which rounded to the closest integer produces 2;
The assembly [a(4),a(5)] is 3.4 which rounded to the closest integer produces 3;
The assembly [a(5),a(6)] is 4.6 which rounded to the closest integer produces 5;
etc.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Apr 18 2019
STATUS
approved