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

0,3

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

Prog

(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])}

Crossrefs

Cf. A254337, A153136.

Sequence in context: A200838 A302160 A122984 * A188477 A302632 A045860

Adjacent sequences: A254338 A254339 A254340 * A254342 A254343 A254344

Keyword

nonn

Author

M. F. Hasler, Jan 29 2015

Status

approved