a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)/3) sets a new record.

Terms

a(0) =3a(1) =7a(2) =29a(3) =113a(4) =523a(5) =1151a(6) =1327a(7) =9551a(8) =15683a(9) =19609a(10) =25471a(11) =31397a(12) =156007a(13) =360653a(14) =370261a(15) =492113a(16) =1349533a(17) =1357201a(18) =1357333a(19) =1562051a(20) =2010733a(21) =4652507a(22) =17051707a(23) =17051887a(24) =20831323a(25) =47326693a(26) =47326913a(27) =122164747a(28) =189695893a(29) =191912783