STATUS
reviewed
approved
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Revision History for A307603
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Lexicographically earliest sequence with no duplicate term that produces only primes by the rounding technique explained in the Comments section.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
CROSSREFS
Cf. A173919 (Numbers that are prime or one less than a prime.).
STATUS
approved
editing
STATUS
editing
approved
COMMENTS
"Rounding to the closest integer" might be seen as is ambiguous for decimal numbers like (k.5) where k is an integer. The tradition wants Here we round such numbers to be rounded to (k+1). This is the case here. Note that the 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,... (the can be divided they are divisible by 3).
EXAMPLE
The assembly [a(1),a(2)] is 1.5 which rounded to the closest integer upwards produces 2;
STATUS
proposed
editing
STATUS
editing
proposed
COMMENTS
"Rounding to the closest integer" might be seen as ambiguous for decimal numbers like (k.5) where k is an integer. The tradition wants such numbers to be rounded to (k+1). This is the case here. Note that 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,... neither (the can be divided by 3).
COMMENTS
"Rounding to the closest integer" might be seen as ambiguous for decimal numbers like (k.5) where k is an integer. The tradition wants such numbers to be rounded to (k+1). This is the case here. Note that 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 becauses because 50, 500, 5000,... are not primes themselves (they end with 0) and so aren't 51, 501, 5001,... neither (the can be divided by 3).
COMMENTS
"Rounding to the closest integer" might be seen as ambiguous for decimal numbers like (k.5) where k is an integer. The tradition wants such numbers to be rounded to (k+1). This is the case here. Note that the only occurrence of such a "rounding ambiguity" in the sequence happens with a(1) = 1 and a(2) = 5. But Indeed, no more (k.5) "dilemmas" like this 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 as becauses 50, 500, 5000,... are not primes themselves and so aren't 51, 501, 5001,... neither.