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

Author

Amarnath Murthy, Sep 27 2002

Keywords

• nonn

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

Examples

			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
		

Links

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

Crossrefs

Cf. A075593, A103824, A103825.

Programs

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

Extensions

Extended by Ray Chandler Feb 16 2005