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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.
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1
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1, 5, 2, 3, 4, 6, 7, 10, 52, 53, 11, 12, 58, 59, 13, 16, 60, 61, 17, 18, 66, 67, 19, 22, 70, 71, 23, 28, 72, 73, 29, 30, 78, 79, 31, 36, 82, 83, 37, 40, 88, 89, 41, 42, 96, 97, 43, 46, 502, 503, 47, 100, 508, 509, 101, 102, 520, 521, 103, 106, 522, 523, 107, 108, 540, 541, 109, 112, 546, 547, 113, 126, 556, 557, 127, 130, 562
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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Cf. A173919 (Numbers that are prime or one less than a prime).
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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