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 A335048 #7 Jul 14 2020 23:48:03
%S A335048 0,3,8,13,22,31,44,57,74,91,112,133,158,183,212,241,274,307,344,381,
%T A335048 422,463,508,553,602,651,704,757,814,871,932,993,1058,1123,1192,1261,
%U A335048 1334,1407,1484,1561,1642,1723,1808,1893,1982,2071,2164,2257,2354,2451,2552
%N A335048 Minimum sum of primes (see Comments).
%C A335048 Out of all permutations of the numbers 1..n such that the sum of all adjacent numbers is a prime (A064821) find the one with the minimum sum of the primes. a(n) is the respective minimum sum or equals zero if a permutation does not exist.
%C A335048 The sum of primes arising from a permutation of 1..n is always equal to n*(n+1) minus the values of the two endpoints, so for n > 1 it is probable that a(n) = n*(n+1) - (n+n-2) if n is odd and a(n) = n*(n+1) - (n+n-1) if n is even. - _Giovanni Resta_, Jun 05 2020
%e A335048 For n = 4 there are 4 permutations: 1234, 1432, 3214, 3412. The one with the minimum sum of 13 (5+3+5) is 3214.
%t A335048 p[n_]:=Permutations[Range[n]];g[n_]:=Min[Total/@Select[Table[Table[
%t A335048 p[n][[j,i]]+p[n][[j,i+1]],{i,1,Length[p[n][[j]]]-1}],{j,1,Length[p[n]]}],AllTrue[#,PrimeQ]&]];g/@Range[7] (* slow, just for demo *)
%t A335048 G[n_] := G[n] = Reap[Do[If[PrimeQ[i + j], Sow[i <-> j]], {i, n}, {j, i-1}]][[2, 1]]; a[n_] := Block[{p = 1 + Boole@OddQ@n, ep, s}, ep = Reverse@ SortBy[ Select[ Tuples[ Range[1, n, p], 2], #[[1]] > #[[2]] &], Total]; s = SelectFirst[ ep, FindHamiltonianPath[G[n], #[[1]], #[[2]]] != {} &, {}]; If[s == {}, 0, n (n + 1) - Total[s]]]; Array[a, 51] (* _Giovanni Resta_, Jun 05 2020 *)
%Y A335048 Cf. A064821, A335047.
%K A335048 nonn
%O A335048 1,2
%A A335048 _Ivan N. Ianakiev_, Jun 05 2020
%E A335048 More terms from _Giovanni Resta_, Jun 05 2020