A111688 Primes and composite numbers alternately in increasing order.

2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 23, 24, 29, 30, 31, 32, 37, 38, 41, 42, 43, 44, 47, 48, 53, 54, 59, 60, 61, 62, 67, 68, 71, 72, 73, 74, 79, 80, 83, 84, 89, 90, 97, 98, 101, 102, 103, 104, 107, 108, 109, 110, 113, 114, 127, 128, 131, 132, 137, 138

Offset

1,1

Comments

3 is the only prime missing. p and p+1 where p is a prime.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(2*n-1) = prime(n+1) for n >= 2; a(2*n) = prime(n+1) for n >= 2. - Andrew Howroyd, Dec 10 2024

Prog

(PARI) a(n)=if(n<3, 2*n, prime((n+3)\2) + (1-n%2)) \\ Andrew Howroyd, Dec 10 2024

Crossrefs

Cf. A000040.

Sequence in context: A324583 A101742 A194831 * A058049 A091871 A303393

Adjacent sequences: A111685 A111686 A111687 * A111689 A111690 A111691

Keyword

easy,nonn

Author

Amarnath Murthy, Aug 17 2005

Extensions

a(57) onwards from Andrew Howroyd, Dec 10 2024

Status

approved