A085417 Take prime[n] and continue adding n,n+1,..., n+a(n)-1 until one reaches a prime.

1, 1, 3, 1, 3, 1, 3, 9, 3, 5, 3, 5, 3, 12, 4, 9, 3, 1, 3, 4, 3, 1, 4, 1, 7, 1, 7, 5, 3, 4, 3, 1, 3, 1, 3, 8, 3, 9, 7, 5, 4, 1, 8, 12, 4, 4, 15, 1, 8, 21, 3, 5, 24, 9, 12, 8, 3, 4, 3, 9, 11, 4, 3, 5, 48, 1, 7, 33, 3, 1, 3, 1, 15, 12, 3, 5, 8, 5, 3, 36, 19, 1, 3, 5, 11, 5, 12, 5, 4, 4, 3, 1, 3, 5, 3, 1, 15, 1

Offset: 1

Author

Zak Seidov, Jun 30 2003

Keywords

• easy
• nonn

Comments

Primes obtained are in A085418. See also A085415, A085416.

No terms == 2 (mod 4). - Robert Israel, Mar 24 2023

Examples

			a(3)=3 because prime[3]=5 and 5+(3+4+5)=17= is a prime A085418(3).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085415, A085416, A085418.

Programs

Maple

f:= proc(n) local m,k,x;
  m:= ithprime(n) - (n-1)*n/2;
  for k from n do
    x:= k*(k+1)/2 + m;
    if isprime(x) then return k+1-n fi
  od;
end proc:
map(f, [$1..100]); # Robert Israel, Mar 24 2023