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 A113843 #12 Jul 10 2015 19:54:52
%S A113843 0,2,3,7,13,29,53,103,199,389,751,1447,2789,5381,10369,19991,38543,
%T A113843 74287,143197,276019,532061,1025579,1976857,3810517,7345031,14158009,
%U A113843 27290429,52604017,101397487,195449957,376741891,726193373,1399782719,2698167947,5200885961
%N A113843 Tetranacci analog of A055502.
%C A113843 This is to the tribonacci sequence as A055502 is to the Fibonacci sequence and A113823 is to the tribonacci sequence (i.e., least prime greater than the sum of the previous 2 terms in A055502, least prime greater than the sum of the previous 3 terms in A113823, least prime greater than the sum of the previous 4 terms in this sequence).
%H A113843 Harvey P. Dale, <a href="/A113843/b113843.txt">Table of n, a(n) for n = 0..1000</a>
%F A113843 a(-n) = a(0) = 0, a(1) = 2, for n>1: a(n) = smallest prime > a(n-1)+a(n-2)+a(n-3)+a(n-4).
%e A113843 a(15) = 19991 because a(11)+a(12)+a(13)+a(14) = 1447 + 2789 + 5381 + 10369 = 19986 and 19991 is the smallest prime > 19986.
%t A113843 nxt[{a_,b_,c_,d_}]:={b,c,d,NextPrime[a+b+c+d]}; Transpose[ NestList[ nxt,{0,2,3,7},40]][[1]] (* _Harvey P. Dale_, Sep 18 2013 *)
%Y A113843 Cf. A055502, A113823.
%K A113843 easy,nonn
%O A113843 0,2
%A A113843 _Jonathan Vos Post_, Jan 24 2006
%E A113843 More terms from _Harvey P. Dale_, Sep 18 2013