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Smallest prime(k) such that prime(k)-prime(k-n) is equal to prime(k+1)-prime(k).
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%I #17 Apr 05 2017 04:48:03

%S 5,7,619,6581,13933,15823,22307,259033,678659,745757,576791,15014557,

%T 35630467,31515413,264426203,356604959,364058659,2529682091,

%U 6868844179,1457908691,12799238129,23294528897,72106293983,82160403553,230966323927,19187736221

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

%H Giovanni Resta, <a href="/A089344/b089344.txt">Table of n, a(n) for n = 1..30</a>

%F a(n) = prime(A066496(n)). - _Giovanni Resta_, Apr 04 2017

%e a(4) = 6581, the next prime is 6599, 6599-6581 = 18, the four previous primes are 6563, 6569, 6571 and 6577. 6581-6563 = 18.

%t f[n_] := Block[{k = n + 1}, While[ 2Prime[k] != Prime[k + 1] + Prime[k - n], k++ ]; Prime[k]]; Table[ f[n], {n, 17}] (* _Robert G. Wilson v_, Nov 11 2003 *)

%Y Cf. A066496, A006562 (balanced primes), A117876, A118467.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Nov 05 2003

%E Corrected and extended by _Ray Chandler_ and _Robert G. Wilson v_, Nov 07 2003

%E a(18)-a(21) from _Fabien Sibenaler_, Mar 15 2013

%E a(22)-a(26) from _Giovanni Resta_, Apr 04 2017