A084833 a(n) is the smallest number such that a(n) + a(n-1), a(n) + a(n-1) + a(n-2), ..., a(n) + ... + a(1) are nonprime.

1, 3, 5, 1, 15, 9, 15, 6, 3, 6, 21, 6, 3, 6, 15, 6, 3, 6, 3, 9, 3, 9, 15, 6, 3, 6, 3, 9, 9, 9, 3, 9, 9, 9, 3, 6, 3, 3, 3, 3, 3, 6, 15, 6, 3, 3, 3, 6, 9, 6, 3, 6, 9, 9, 3, 6, 3, 6, 15, 6, 3, 6, 3, 9, 3, 9, 3, 9, 9, 6, 3, 6, 9, 6, 3, 3, 3, 6, 3, 9, 3, 6, 3, 3, 3, 6, 3, 6, 3, 6, 9, 6, 3, 3, 3, 6, 9, 6, 3

Offset: 1

Author

Jon Perry, Jun 06 2003

Keywords

• nonn

Comments

No sum of a continuous subsequence is ever prime. Does the sequence consist only of multiples of 3 after a(4)?

Examples

			a(5) = 15 as 1+3+5+1+15 = 25 is composite, 3+5+1+15 = 24 is composite, 5+1+15 = 21 is composite, and 1+15 = 16 is composite, and no smaller number has this property.
		

Crossrefs

Cf. A084834.

Programs

PARI

{ checkprime(a,b)=local(fl); fl=0; for (i=1,b-1,if (isprime(a+s[i]),fl=1; break)); fl }
{ p=vector(100); p[1]=1; pc=2; while (pc<100, x=1; s=vector(100); for (i=1,pc-1,s[i]=sum(k=i,pc-1,p[k])); i=1; while (checkprime(x,pc),x++); p[pc]=x; pc++); p }