|
%I #28 Mar 12 2015 20:01:28
%S 5,11,29,97,641,1373,2591,4327,8009,19661,36451,134581,38543,172969,
%T 212777,268403,1784171,860239,1562053,6085103,6958813,3422971,5103029,
%U 14723567,47973451,38394329,36271783,75837497,59160181,47326919,111660697,369706811,323627951
%N a(n) is the smallest prime(i) such that (prime(i) - prime(j))/(i - j) = prime(n) with i > j.
%C (i - j) = 2 for all the calculated terms, with the exception of a(1) where (i - j) = 1 and a(6) where (i - j) = 4.
%e a(3) = 29 is the smallest prime (and 10th prime) such that there is a smaller 8th prime: 19 and (29 - 19) / (10 - 8) = 5 is the third prime.
%t a[1]=5; a[n_] := Catch[Block[{r = Prime@n, i=2, j, p}, While[True, p = Prime[++i]; j = Mod[i, 2]; While[(j += 2) < i, If[p - Prime@j == r*(i-j), Throw@p]]]]] (* _Giovanni Resta_, Dec 28 2013 *)
%o (PARI) n=16;c=25000;for(b=2,c,forstep(a=b+2,c,2,d=prime(a)-prime(b);e=(a-b);if(d/e==d\e&d/e==prime(n),print([a,b,prime(a),prime(b),d,e,d/e])))) \\ finds a(16) and in general a(n).
%o (PARI) okp(n, p) = {i = primepi(p); forprime (q = 2, p-1, j = primepi(q); if ((p-q)/(i-j) == prime(n), return(1)););}
%o a(n) = {p = 2; while (! okp(n, p), p = nextprime(p+1)); p;} \\ _Michel Marcus_, Dec 28 2013
%K nonn
%O 1,1
%A _Robin Garcia_, Dec 27 2013
%E a(17)-a(25) from _Giovanni Resta_, Dec 28 2013
%E a(26)-a(33) from _Donovan Johnson_, Jan 01 2014
|
