A122498
Padovan numbers that are semiprimes.
Original entry on oeis.org
4, 9, 21, 49, 65, 86, 265, 1081, 1897, 2513, 7739, 97229, 128801, 299426, 922111, 1221537, 2839729, 62608681, 338356945, 53406819691, 2066337330754, 6363483400447, 8429820731201, 432062194544201, 7190854504969591, 12619069972000553, 16716708595637087
Offset: 1
-
select(x-> numtheory[bigomega](x)=2, [(<<0|1|0>,
<0|0|1>, <1|1|0>>^i)[1$2]$i=0..300])[]; # Alois P. Heinz, Aug 31 2017
-
SemiprimeQ[1] := False SemiprimeQ[n_Integer] := Plus @@ (Last /@ FactorInteger[n]) == 2 a = Table[ SeriesCoefficient[ Series[x/(1 - x^2 - x^3), {x, 0, 50}], n], {n, 0, 50}] f[n_] = If[SemiprimeQ[a[[n]]] == True, a[[n]], {}] Flatten[Table[f[n], {n, 1, Length[a]}]]
A112882
Indices of prime Padovan numbers: values of k such that A000931(k+5) is prime.
Original entry on oeis.org
3, 4, 5, 7, 8, 14, 19, 30, 37, 84, 128, 469, 666, 1262, 1573, 2003, 2210, 2289, 4163, 5553, 6567, 8561, 11230, 18737, 35834, 44259, 536485, 727734
Offset: 1
A291216
Padovan numbers that are also squares.
Original entry on oeis.org
0, 1, 4, 9, 16, 49
Offset: 1
- Ian Stewart, Tales of a Neglected Number, Mathematical Recreations, Scientific American, June 1996.
- Ian Stewart, Tales of a Neglected Number, Mathematical Recreations, Scientific American, Vol. 274, No. 6 (1996), pp. 102-103.
- Ian Stewart, Die unscheinbare Schwester der goldenen Zahl, Spektrum der Wissenschaft, Dossier 02/2003: Mathematische Unterhaltungen II, 55-57.
A291673
Padovan numbers that are also Fibonacci numbers.
Original entry on oeis.org
0, 1, 2, 3, 5, 21
Offset: 1
-
With[{nn=100},Join[{0},Intersection[LinearRecurrence[{0,1,1},{1,1,2},nn],Fibonacci[Range[nn]]]]] (* Harvey P. Dale, Oct 09 2017 *)
A152870
Indices of primes in the Padovan sequence A000931.
Original entry on oeis.org
8, 9, 10, 12, 13, 19, 24, 35, 42, 89, 133, 474, 671, 1267, 1578, 2008, 2215, 2294, 4168, 5558, 6572, 8566, 11235, 18742, 35839, 44264, 536490, 727739
Offset: 1
-
a[0] = 1; a[1] = 0; a[2] = 0;
a[n_] := a[n] = a[n - 2] + a[n - 3];
Flatten[Table[If[PrimeQ[a[n]], n, {}], {n, 0, 10000}]]
-
v=[1,1,1];for(n=8,1e4,v=[v[2],v[3],v[1]+v[2]];if(ispseudoprime(v[3]),print1(n", "))) \\ Charles R Greathouse IV, Nov 07 2011
Showing 1-5 of 5 results.
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