A192574 -id:A192574 - cp's OEIS frontend

A192596 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+4y is a prime, then 3x+4y is in S, and 1 is in S.

1, 7, 31, 97, 127, 409, 601, 769, 1231, 1657, 1831, 2017, 2311, 3079, 3169, 3457, 3631, 3697, 3943, 4201, 4999, 5479, 5521, 5881, 6079, 6151, 6607, 6961, 7057, 7129, 7321, 7417, 7687, 8089, 8161, 8431, 9127, 9241, 9337, 9511, 9631, 9871, 10009

Offset: 1

Clark Kimberling, Jul 05 2011

nonn

See the discussions at A192476 and A192580.

Cf. A192574, A192580, A192597.

start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, 3 x + 4 y], 3 x + 4 y]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
         Length[w]}]]]], # < 20000 &]];
t = FixedPoint[b, start]    (* A192596 *)
PrimePi[t]   (* A192597 *)

A192576 a(n) = sum(binomial(n,k)*floor(sqrt(Bell(k))),k=0..n).

Original entry on oeis.org

1, 2, 4, 9, 22, 58, 163, 478, 1439, 4415, 13780, 43757, 141400, 465016, 1555961, 5294885, 18315089, 64357854, 229601019, 831132731, 3051030786, 11351968321, 42788503744, 163309466037, 630861836558, 2465577001903, 9745376900983

Offset: 0

Emanuele Munarini, Jul 04 2011

nonn

Cf. A192570, A192571, A192572, A192573, A192574.

The Bell numbers are A000110.

Table[Sum[Binomial[n,k]Floor[Sqrt[BellB[k]]],{k,0,n}],{n,0,100}]

makelist(sum(binomial(n,k)*floor(sqrt(belln(k))),k,0,n),n,0,28);

cp's OEIS Frontend

A192596 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+4y is a prime, then 3x+4y is in S, and 1 is in S.

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