A085415 Take prime[n] and continue adding 1, 2, ..., a(n) until one reaches a prime.

1, 4, 3, 3, 3, 3, 3, 4, 3, 12, 3, 3, 3, 4, 3, 3, 12, 3, 3, 8, 3, 4, 3, 12, 3, 3, 3, 3, 7, 8, 4, 3, 8, 4, 12, 3, 3, 4, 3, 3, 12, 4, 3, 3, 8, 7, 7, 3, 3, 4, 3, 12, 4, 3, 3, 3, 12, 3, 3, 8, 4, 11, 3, 3, 8, 8, 3, 4, 3, 4, 3, 15, 3, 3, 4, 3, 12, 8, 11, 4, 24, 4, 8, 3, 4, 3, 15, 3, 3, 7, 8, 12, 8, 11, 4, 3, 12, 8

Offset: 1

Author

Zak Seidov, Jun 29 2003

Keywords

• easy
• nonn

Comments

Resulting primes in A085416. See also A085417, A085418.

Prime[n] plus a triangular number is prime. - Harvey P. Dale, Jun 12 2013

Examples

			a(2)=4 because prime[2]+(1+2+3+4)=3+10=13 is a prime
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A085416, A085417, A085418.

Programs

Mathematica

Flatten[(Sqrt[1+8#]-1)/2&/@With[{trnos=Accumulate[Range[30]]}, Table[ Select[ trnos,PrimeQ[Prime[n]+#]&,1],{n,100}]]] (* Harvey P. Dale, Jun 12 2013 *)

Formula

Prime[n]+m*(1+m)/2 is a prime for some m>0.