%I #12 Dec 02 2023 14:54:50

%S 0,1,2,4,9,10,30,35,36,56,86,109,158,195,213,287,331,373,409,432,462,

%T 579,638,656,722,749,894,1154,1177,1225,1304,1414,1416,1550,1800,1844,

%U 2091,2114,2351,2851,4218,4344,4658,5054,5627,5836,7092,7997,8204,8324,8889,9527

%N "Orders" where balanced prime number records (A082080) occur.

%F a(n) = A082080(A096266(n)).

%t f[n_] := Block[{k = n + 2, s = Plus @@ Table[ Prime[i], {i, 2, 2n + 2}]}, While[s != (2n + 1)Prime[k], k++; s = s - Prime[k - n - 1] + Prime[k + n]]; Prime[k]]; p = 1; Do[ q = f[n]; If[q > p, Print[n, " = ", q]; p = q], {n, 1230}]

%Y Cf. A082080, A096266.

%K nonn

%O 1,3

%A _Robert G. Wilson v_, Jun 26 2004

%E a(31)-a(52) from _Robert Price_, Dec 02 2023