A308319 Lexicographically earliest sequence of distinct terms starting with a prime such that one of the terms of {a(n), a(n+1)} is prime and the other not, with [a(n) + a(n+1)] = nonprime.

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

Offset

1,1

Comments

This is probably a permutation of the positive integers.

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

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

Links

Carole Dubois, Table of n, a(n) for n = 1..1338

Example

The sequence starts with 2, 4, 5, 1, 3, 6, 19, 8, 7, ... and we see that:
a(1) + a(2) = 2 + 4 = 6 (nonprime sum of a prime and a nonprime);
a(2) + a(3) = 4 + 5 = 9 (nonprime sum of a nonprime and a prime);
a(3) + a(4) = 5 + 1 = 6 (nonprime sum of a prime and a nonprime);
a(4) + a(5) = 1 + 3 = 4 (nonprime sum of a nonprime and a prime);
a(5) + a(6) = 3 + 6 = 9 (nonprime sum of a prime and a nonprime); etc.

Crossrefs

Cf. A308315 (an equivalent sequence that starts with a nonprime).

Sequence in context: A036501 A225153 A360108 * A167380 A242613 A196548

Adjacent sequences: A308316 A308317 A308318 * A308320 A308321 A308322

Keyword

nonn

Author

Carole Dubois and Eric Angelini, May 20 2019

Extensions

Comments corrected by Rémy Sigrist, May 22 2019

Status

approved