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%I #13 Aug 28 2024 23:11:26
%S 113,199,317,619,863,1069,1129,1789,2861,3089,3169,3259,3677,3739,
%T 4733,4973,5419,5591,6581,7649,7963,8243,8297,8629,9973,10463,10799,
%U 10909,11093,11119,12347,12379,12619,12983,14011,14327,15331,15649,16007
%N Primes that represent some mean of 4 consecutive (2 smaller, itself, 1 larger) primes.
%C A prime number prime(n) is in the sequence if the arithmetic mean of the 4 nearby primes, measured by A034963(n-2)/4, equals one plus the prime. - _R. J. Mathar_, Nov 15 2019
%e 113 is in the list because the arithmetic mean of 107, 109, 113, and 127 is A034963(28)/4 = 456/4 = 114, and 114 = 1+113.
%t a=Table[If[(Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-1]-1==0, Prime[n-1], 0], {n, 4, 2004}] a0=Delete[Union[Sort[a]], 1]
%K nonn,less
%O 4,1
%A _Roger L. Bagula_, Jun 17 2004
%E Definition rephrased. - _R. J. Mathar_, Nov 15 2019