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.
a={1,8,8}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
a246517 n = a246517_list !! (n-1) a246517_list = filter ((== 1) . a010051'' . a141036) [0..] -- Reinhard Zumkeller, Sep 15 2014
a={2,1,1}; Print[0]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
Let S(n) = row n of A381801 and R(n) = row n of A162306, with n in R(n) instead written as n mod n = 0.
Define quality Q between natural numbers k and n to be rad(k) does not divide n.
a(10) = 1 since S(10) = {0,1,2,4,5,6,8} only contains r = 6 with quality Q.
a(15) = 3 since S(15) = {0,1,3,5,6,9,10,12} and R(15) = {0,1,3,5,9} = {6,10,12}.
a(18) = 2 since S(18) = {0,1,2,3,4,6,8,9,10,12,14,16} and R(18) = {1,2,3,4,6,8,9,12,16,18} = {10,14}.
a(20) = 1 since S(20) = {0,1,2,4,5,8,10,12,16} and R(20) = {0,1,2,4,5,8,10,16} = {12}, etc.
f[x_] := Block[{c, ff, m, r, p, s, w},
c[_] := True; ff = FactorInteger[x][[All, 1]]; w = Length[ff];
s = {1};
Do[Set[p[i], ff[[i]]], {i, w}];
Do[Set[s, Union@ Flatten@ Join[s, #[[-1, 1]]]] &@ Reap@
Do[m = s[[j]];
While[Sow@ Set[r, Mod[m*p[i], x]];
c[r],
c[r] = False;
m *= p[i]],
{j, Length[s]}],
{i, w}]; s ];
rad[x_] := Times @@ FactorInteger[x][[All, 1]];
{0}~Join~Table[Length@ Complement[f[n], {0}~Join~Select[Range[n - 1], Divisible[#, rad[#]] &]], {n, 2, 120}]
a={1,9,9}; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]
Flatten[Position[LinearRecurrence[{1,1,1},{1,9,9},200000],?PrimeQ]]-1 (* The prime number at index 195346 (term a(39) of this sequence) has 51699 digits, so this program takes a long time to run. *) (* _Harvey P. Dale, Dec 29 2019 *)
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