This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337306 #32 Nov 21 2020 21:36:03
%S A337306 2,37,557,647,9803,192583,698653,150287,34449209,136017109,191058199,
%T A337306 618408991,564779279,40434774727,52195951979,149416079731,
%U A337306 598718776379,802636910771
%N A337306 a(n) is the least start of a run of exactly n consecutive prime numbers which are digitally balanced numbers in base 2 (A031443).
%e A337306 a(1) = 2 since 2 is a prime and a digitally balanced number and the next prime, 3, is not.
%e A337306 a(2) = 37 since 37 is a prime, 37 and the next prime, 41, are both digitally balanced in base 2, and the primes previous to 37 (31) and next to 41 (43) are not.
%t A337306 digBalQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ@(m = Length@d) && Count[d, 1] == m/2]; s[max_] := Module[{seq = Table[0, {max}], count = 0, p = 2, pp, n}, While[count < max, If[digBalQ[p], pp = NextPrime[p]; n = 1; While[digBalQ[pp], n++; pp = NextPrime[pp]]; If[n <= max && seq[[n]] == 0, count++; seq[[n]] = p]; p = NextPrime[pp], p = NextPrime[p]]]; seq]; s[8]
%Y A337306 Cf. A031443, A066196, A337258.
%K A337306 nonn,base,more
%O A337306 1,1
%A A337306 _Amiram Eldar_, Nov 21 2020