A278007 Lexicographically first sequence of primes (with no duplicates) whose absolute first differences are nonprime (with no duplicates).

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

Offset

1,1

Comments

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.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

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.

Crossrefs

Cf. A277997.

Sequence in context: A249051 A329413 A225093 * A081256 A084955 A273056

Adjacent sequences: A278004 A278005 A278006 * A278008 A278009 A278010

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Nov 08 2016

Status

approved