A085415 - OEIS

%I #8 Jun 12 2013 15:00:16

%S 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,

%T 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,

%U 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

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

%C Resulting primes in A085416. See also A085417, A085418.

%C Prime[n] plus a triangular number is prime. - _Harvey P. Dale_, Jun 12 2013

%H Harvey P. Dale, <a href="/A085415/b085415.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%t 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 *)

%Y Cf. A085416, A085417, A085418.

%K easy,nonn

%O 1,2

%A _Zak Seidov_, Jun 29 2003