A084834 a(n) is the smallest number not previously used such that a(n)+a(n-1), a(n)+a(n-1)+a(n-2), ..., a(n)+...+a(1) are not prime.

1, 3, 5, 7, 9, 11, 13, 15, 17, 4, 6, 30, 38, 10, 36, 14, 34, 42, 39, 21, 69, 27, 33, 45, 20, 16, 24, 50, 25, 51, 66, 18, 72, 54, 60, 74, 22, 8, 19, 41, 28, 48, 44, 40, 78, 57, 35, 58, 102, 12, 63, 65, 64, 56, 46, 96, 68, 76, 114, 80, 52, 84, 90, 99, 55, 2, 93, 75, 100, 62, 120, 98

Offset: 1

Author

Jon Perry, Jun 06 2003

Keywords

• nonn

Comments

No sum of a continuous subsequence is ever prime. Is every integer used? Can an odd number ever be surrounded by two even numbers (and similarly for even numbers)?

Examples

			a(4)=7 because 7 is the smallest unused number such that 1+3+5+x, 3+5+x and 5+x are all composite
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A084833, A254337.

Programs

PARI

checkprime(a,b)=local(fl); fl=0; for (i=1,b-1,if (isprime(a+s[i]),fl=1; break)); if (fl==0, for (j=1,b-1,if (a==p[j],fl=1; break))); fl
p=vector(300); p[1]=1; pc=2; while (pc<300, x=1; s=vector(300); 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