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A278007
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Lexicographically first sequence of primes (with no duplicates) whose absolute first differences are nonprime (with no duplicates).
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1
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2, 3, 7, 13, 5, 17, 31, 11, 29, 19, 41, 67, 23, 47, 79, 37, 53, 83, 43, 71, 107, 59, 97, 131, 61, 113, 163, 73, 127, 173, 89, 149, 211, 101, 157, 223, 103, 167, 109, 181, 257, 139, 227, 307, 137, 229, 151, 233, 331, 179, 281, 349, 191, 277, 373, 193, 293, 199, 311, 197, 271
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OFFSET
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1,1
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COMMENTS
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The sequence starts with a(1) = 2 and is always extended with the smallest integer not yet present that does not lead to a contradiction.
The equivalent sequence where nonprimes and primes exchange their roles is A277997.
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LINKS
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EXAMPLE
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After a(1) = 2, we cannot have a(2) = 1 as 1 is not a prime number; a(2) = 3 is OK as the absolute difference |2-3| = 1 is a nonprime; the next term a(3) cannot be 5 as the absolute difference |3-5| = 2 is a prime (and we don't want primes in the absolute differences); a(3) = 7 is OK as the absolute difference |3-7| = 4 is a nonprime not yet present in the absolute differences; the next term a(4) cannot be 5 as the absolute difference |7-5| = 2 is a prime; the next term a(4) cannot be 11 as the absolute difference |7-11| = 4 is already in the absolute differences, a(4) = 13 is OK as the absolute difference |7-13| = 6 is a nonprime not yet present in the absolute differences; the next term a(5) is now 5 as |13-5| = 8 is a nonprime not yet present in the absolute differences; the next term a(6) cannot be 11, the smallest available prime, as the absolute difference |5-11| = 6 is a nonprime already present in the absolute differences; a(6) = 17 is OK as |5-17| = 12 is a nonprime not yet present in the absolute differences; the next term a(7) cannot be 11, 19, 23 or 29 for one of the above reasons, but a(7) = 31 is OK as |17-31| = 14 is a nonprime not yet present in the absolute differences; etc.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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