A066753 a(n) = least natural number k such that n + Sum_{i=1..k} prime(i) is prime if such k exists; = 0 otherwise.

1, 2, 1, 20, 1, 2, 3, 2, 1, 10, 1, 2, 3, 2, 1, 16, 1, 2, 3, 4, 1, 10, 17, 2, 5, 2, 1, 10, 1, 4, 3, 2, 3, 10, 1, 2, 3, 2, 1, 16, 1, 2, 3, 4, 1, 18, 17, 2, 3, 4, 1, 10, 41, 2, 5, 2, 1, 16, 1, 6, 3, 2, 3, 10, 1, 2, 9, 2, 1, 10, 1, 4, 3, 2, 5, 16, 1, 2, 3, 4, 1, 10, 17, 2, 5, 4, 1, 20, 43, 4, 3, 2, 3, 10

Offset

1,2

Comments

Does a(n) ever take 0 as a value?

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

20 + (2 + 3 + 5 + 7) = 37, a prime and 4 consecutive primes starting with 2 are required to achieve this. So a(20) = 4.

Mathematica

nt = 200; a = Table[0, {i, 1, nt}]; For[n = 1, n <= nt, n++, {i = 1; s = n + Prime[i]; While[Not[PrimeQ[s]] && (i < 1000), {i++; s = s + Prime[i]}]; a[[n]] = i}]; a

Prog

(PARI) { for (n=1, 1000, k=0; b=0; s=n; while(b==0, k++; s+=prime(k); if (isprime(s), b=1)); write("b066753.txt", n, " ", k) ) } \\ Harry J. Smith, Mar 22 2010

Crossrefs

Sequence in context: A013021 A012907 A317996 * A103244 A328921 A185169

Adjacent sequences: A066750 A066751 A066752 * A066754 A066755 A066756

Keyword

nonn

Author

Joseph L. Pe, Jan 16 2002

Extensions

Edited by John W. Layman, Jan 23 2002

Status

approved