A075594 a(1) = 1, a(2n) = composite, a(2n+1) = prime and sum of two successive terms is alternately prime or composite.

1, 4, 2, 9, 3, 8, 7, 6, 19, 10, 5, 12, 13, 16, 11, 18, 17, 14, 31, 22, 23, 20, 29, 24, 41, 26, 37, 30, 47, 32, 43, 28, 53, 36, 59, 38, 61, 40, 71, 42, 73, 34, 83, 44, 67, 46, 79, 48, 97, 52, 89, 50, 103, 54, 101, 56, 109, 58, 107, 60, 127, 64, 113, 66, 137, 62, 139, 72, 131

Offset

1,2

Comments

Conjecture: a(n+r)= A075593(n) for n > k for some k and r. What is the value of k and r?

This is not a permutation of the positive integers; odd composites > 9 will not appear in the sequence. - Klaus Brockhaus, Feb 06 2006

Links

Bill McEachen, Table of n, a(n) for n = 1..10000

Example

After terms 1, 4, 2, 9, 3, we seek the next term (n = 6). The requirement is the smallest composite not already seen that summed with a(5) is prime. That number is 8 and becomes a(6). Similarly, for n = 7, we require the smallest prime not already seen that summed with a(6) is composite. As 8 + 5 is not composite, a(7) = 7. - Bill McEachen, Feb 13 2023

Prog

(PARI) genit(nterms=69)={arr=List(); listput(arr, 1); listput(arr, 4); summ=arr[#arr]+arr[#arr-1]; for(ptr=3, +oo, if(#arr>nterms, break); for(i=2, +oo, if(ptr%2!=0&&isprime(i), q=arr[ptr-1]+i; z=Set(arr); if(setsearch(z, i)>0, next); z=Set(); if(isprime(summ)&& !isprime(q), listput(arr, i); summ=arr[#arr]+arr[#arr-1]; break)); if(ptr%2==0&&!isprime(i), q=arr[ptr-1]+i; z=Set(arr); if(setsearch(z, i)>0, next); z=Set(); if(!isprime(summ)&& isprime(q), listput(arr, i); summ=arr[#arr]+arr[#arr-1]; break)))); arr} \\ Bill McEachen, Apr 09 2023

Crossrefs

Cf. A075593, A103824, A103825.

Sequence in context: A095303 A060734 A375719 * A076022 A064421 A051494

Adjacent sequences: A075591 A075592 A075593 * A075595 A075596 A075597

Keyword

nonn

Author

Amarnath Murthy, Sep 27 2002

Extensions

Extended by Ray Chandler Feb 16 2005

Status

approved