

A084834


a(n) is the smallest number not previously used such that a(n)+a(n1), a(n)+a(n1)+a(n2), ..., a(n)+...+a(1) are not prime.


5



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
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OFFSET

1,2


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)?


LINKS

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


EXAMPLE

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


PROG

(PARI) checkprime(a, b)=local(fl); fl=0; for (i=1, b1, if (isprime(a+s[i]), fl=1; break)); if (fl==0, for (j=1, b1, 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, pc1, s[i]=sum(k=i, pc1, p[k])); i=1; while (checkprime(x, pc), x++); p[pc]=x; pc++); p


CROSSREFS

Cf. A084833, A254337.
Sequence in context: A187232 A187907 A024806 * A118137 A160931 A160924
Adjacent sequences: A084831 A084832 A084833 * A084835 A084836 A084837


KEYWORD

nonn


AUTHOR

Jon Perry, Jun 06 2003


STATUS

approved



