A249064 Lexically first sequence of distinct positive integers such that a(n) is coprime to the next a(n) elements.

1, 2, 3, 5, 4, 7, 9, 11, 13, 8, 17, 19, 23, 25, 29, 31, 21, 37, 16, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 22, 109, 113, 27, 35, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 32, 121, 223, 227, 229, 233, 239, 241, 51, 251, 257, 263, 269, 271, 277, 281, 283, 49, 95

Offset: 1

Author

Hugo van der Sanden, Oct 20 2014

Keywords

• nonn

Comments

Described in this form, A090252 would be "lexically first sequence of positive integers such that a(n) is coprime to the next n elements".

(And A247665 would be "lexically first sequence of integers >= 2 such that a(n) is coprime to the next n elements". - N. J. A. Sloane, Nov 01 2014)

All values up to a(1000000) are either prime powers or semiprimes, except when n is in (868, 947, 993, 1069, 1205, 1431, 854300) with values respectively (172, 45, 75, 135, 225, 375, 9475). This suggests the sequence is unlikely to be a permutation of the integers.

If, mimicking A247665, one starts with a(1)=2 and uses the same rule (always using distinct numbers >= 2) one obtains A249064 again, without the leading 1. - N. J. A. Sloane, Nov 01 2014

Links

• Hugo van der Sanden, Table of n, a(n) for n = 1..1001
• Hugo van der Sanden, Perl program to calculate this sequence and A090252 (requires Math::Pari)
• Hugo van der Sanden, Faster Perl program on github.

Crossrefs

Cf. A090252, A247665, A249557.

Extensions

Added "distinct" to the definition. - Hugo van der Sanden, Oct 28 2014