login
Smallest prime(k) such that prime(k)-prime(k-1) is equal to prime(k+n)-prime(k).
0

%I #7 Dec 02 2018 03:08:20

%S 5,37,1009,4327,6197,6947,43391,31469,1324567,678719,6655531,1895479,

%T 6085103,21500429,93685619,523000399,20388727,709208557

%N Smallest prime(k) such that prime(k)-prime(k-1) is equal to prime(k+n)-prime(k).

%C Cf. A089344.

%e a(4) = 4327, the previous prime is 4297, 4327-4297 = 30, the next four primes are 4337, 4339, 4349 and 4357. 4357-4327 = 30.

%t f[n_] := Block[{k = n + 1}, While[ 2Prime[k] != Prime[k - 1] + Prime[k + n], k++ ]; Prime[k]]; Table[ f[n], {n, 18}]

%o (PARI) a(n)=local(k=1);if(n<1,0,until(prime(k)-prime(k-1)==prime(k+n)-prime(k),k++);prime(k)) /* _Michael Somos_, Feb 01 2004 */

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Nov 11 2003