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 A088614 #9 Mar 28 2015 17:42:22
%S A088614 2,9,3,27,11,51,13,33,41,93,31,99,29,63,1117,441,503,303,163,171,59,
%T A088614 357,67,219,113,417,691,729,239,511,227,393,211,189,3797,291,1789,549,
%U A088614 419,501,103,81,3257,39,727,531,617,69,6883,387,521,153,1237,287,3391,927
%N A088614 Alternate prime and composite numbers not included earlier such that every partial concatenation is a prime: a(2n) is composite and a(2n-1) is prime.
%C A088614 Conjecture: 1 and 5 are the only two odd nonmembers.
%e A088614 2,29,293,29327,...etc. are primes.
%t A088614 p = Prime[ Range[ 1000]]; np = Complement[ Range[ 1000], p]; a[n_] := a[n] = Block[{k = 1, q = Flatten[ IntegerDigits[ # ] & /@ Table[ a[i], {i, n - 1}]]}, If[ OddQ[n], While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ p[[k]] ]]]], k++ ]; q = p[[k]]; p = Delete[p, k]; q, While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ np[[k]] ]]]], k++ ]; q = np[[k]]; np = Delete[np, k]; q]]; Table[ a[n], {n, 56}] (* _Robert G. Wilson v_, Apr 23 2004 *)
%Y A088614 Cf. A088615.
%K A088614 base,nonn
%O A088614 1,1
%A A088614 _Amarnath Murthy_, Oct 16 2003
%E A088614 More terms from _Ray Chandler_, Oct 18 2003