A254341 Lexicographically earliest sequence of distinct numbers with alternating parity such that no sum of consecutive terms is prime.

0, 1, 8, 25, 24, 27, 6, 9, 30, 15, 42, 39, 18, 21, 36, 33, 60, 35, 16, 69, 48, 63, 12, 51, 66, 45, 72, 87, 54, 93, 78, 81, 90, 57, 84, 75, 114, 111, 96, 99, 120, 105, 102, 117, 144, 123, 108, 129, 126, 135, 138, 147, 150, 141, 162, 153, 156, 159, 132, 171, 174, 165, 168, 177, 192, 183, 180, 189, 186, 195, 198, 207, 204, 201, 216, 213, 228, 219, 210, 231, 222, 249, 240, 237, 252, 243, 258, 255, 234, 261, 246, 225, 288, 267, 264, 273, 276, 279, 270

Offset: 0

Author

M. F. Hasler, Jan 29 2015

Keywords

• nonn

Comments

In other words, no sum a(i)+a(i+1)+a(i+2)+...+a(j) may be prime. In particular, the sequence may not contain any primes.

Without the condition that the parity alternates, it seems that the sequence (A254337) contains only a single odd number.

It appears that a(n) ~ 3n. Is there a simple explanation for this?

Links

• M. F. Hasler, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A254337, A153136.

Programs

PARI

{N=10^3; a=[]; u=0; for(i=0,N, a=concat(a,i%2); until( ! isprime(s) || ! a[#a]+=2, while( isprime(a[#a]) || bittest(u,a[#a]), a[#a]+=2);  s=a[k=#a]; while( k>1 && ! isprime( s+=a[k--]),)); u+=2^a[#a])}