A308315 Lexicographically earliest sequence of different terms starting with a nonprime such that one of the terms of {a(n), a(n+1)} is prime and the other not, with [a(n) + a(n+1)] = a nonprime.

1, 3, 6, 2, 4, 5, 9, 7, 8, 13, 12, 23, 10, 11, 14, 19, 15, 17, 16, 29, 20, 31, 18, 37, 21, 41, 22, 43, 25, 47, 27, 53, 24, 61, 26, 59, 28, 67, 32, 73, 33, 71, 34, 83, 35, 79, 36, 89, 30, 103, 38, 97, 39, 101, 40, 107, 45, 109, 44, 127, 42, 113, 46, 131, 49, 137, 48, 139, 50, 151, 51, 149, 52, 157, 55, 163, 54, 167, 57, 173, 58, 179, 56

Offset

1,2

Comments

This is likely a permutation of the positive integers.

a(2*n) is always a prime. - Sean A. Irvine, May 21 2019

a(2*n+1) is always a nonprime. - Sean A. Irvine, May 21 2019

Links

Carole Dubois, Table of n, a(n) for n = 1..1339

Example

The sequence starts with 1,3,6,2,4,5,9,7,... and we see that:
a(1) + a(2) = 1 + 3 = 4 (nonprime sum of a nonprime and a prime);
a(2) + a(3) = 3 + 6 = 9 (nonprime sum of a prime and a nonprime);
a(3) + a(4) = 6 + 2 = 8 (nonprime sum of a nonprime and a prime);
a(4) + a(5) = 2 + 4 = 6 (nonprime sum of a prime and a nonprime);
a(5) + a(6) = 4 + 5 = 9 (nonprime sum of a nonprime and a prime); etc.

Crossrefs

Cf. A308319 (an equivalent sequence that starts with a prime).

Sequence in context: A016614 A019769 A092948 * A200474 A154858 A169837

Adjacent sequences: A308312 A308313 A308314 * A308316 A308317 A308318

Keyword

nonn

Author

Carole Dubois and Eric Angelini, May 19 2019

Status

approved