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
Keywords
Examples
20 + (2 + 3 + 5 + 7) = 37, a prime and 4 consecutive primes starting with 2 are required to achieve this. So a(20) = 4.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
Programs
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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 -
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
Extensions
Edited by John W. Layman, Jan 23 2002
Comments