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 A181437 #34 Apr 06 2022 03:35:25
%S A181437 4,57,57,421,421,1860,1860,24661,24661,380028,380028,2964603,2964603
%N A181437 Size of the longest increasing sequence of primes starting with 2, 3 and with second-order differences bounded by n.
%C A181437 For n > 1, a(2n + 1) = a(2n) because after the primes (2,3,5), all second differences are even numbers. It is not known if the sequence remains finite for all n.
%C A181437 To give an idea of the size of the sequences, the largest prime in the sequence corresponding to a(12) is 1280522207.
%C A181437 For a given n, the Mathematica program uses recursion to find the longest list of primes with second differences bounded by n. This is not the best language to use for this problem. Even n=4 takes quite a while. The program prints longer lists as they are found. - _T. D. Noe_, Feb 03 2011
%H A181437 MathOverflow, <a href="http://mathoverflow.net/questions/53549">Is there an infinite increasing sequence of primes with bounded second or larger differences</a>
%H A181437 Esteban Crespi de Valldaura, <a href="/A181437/a181437.cpp.txt">C++ program used in computations.</a>
%e A181437 For n = 1, the sequence is (2, 3, 5, 7) which has 4 members, so a(1) = 4.
%e A181437 For n = 2, a sequence is (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1597, 1669, 1741, 1811, 1879, 1949, 2017, 2083) which has 57 members, so a(2) = 57.
%t A181437 Valid[lst_List]:=Module[{r1,r2}, r1=-n+2*lst[[-1]]-lst[[-2]]; r2=r1+2*n; r1=Max[lst[[-1]]+1,r1]; Select[Range[r1,r2],PrimeQ]]; FindPath[lst_List]:=Module[{p,ln}, p=Valid[lst]; If[p=={}, ln=Length[lst]; If[ln>len, len=ln; Print[{len,lst}]], Do[FindPath[Append[lst,i]], {i,p}]]]; n=2; len=0; t={2,3}; FindPath[t]; len (* _T. D. Noe_, Feb 03 2011 *)
%K A181437 nonn,nice,more
%O A181437 1,1
%A A181437 _Esteban Crespi de Valldaura_, Jan 31 2011, Feb 03 2011