A117851 Numbers j such that j^3 is of the form semiprime(k) + k-th composite number.

2, 3, 4, 6, 7, 10, 29, 30, 33, 35, 36, 41, 42, 46, 53, 61, 72, 74, 77, 82, 88, 99, 106, 121, 123, 127, 133, 146, 150, 159, 164, 170, 175, 180, 194, 214, 221, 231, 233, 248, 257, 262, 267, 271, 274, 278, 287, 289, 290, 303, 304, 308, 311, 316, 318, 324

Offset

1,1

Comments

Corresponding k's: 1, 6, 15, 50, 78, 219, 4803, 5303, 6973, 8261, 8968, 13058, 13972, 18210, 27426, 41167, ...,.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A112662(n)^(1/3).

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; SemiPrimePi[n_] := Sum[PrimePi[n/Prime@i] - i + 1, {i, PrimePi@Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; lst = {}; Do[c = Composite@n + SemiPrime@n; If[IntegerQ[c^(1/3)], Print[c]], {n, 10^7}]; lst (* Robert G. Wilson v *)

Crossrefs

Sequence in context: A272766 A271340 A362851 * A050679 A342684 A344625

Adjacent sequences: A117848 A117849 A117850 * A117852 A117853 A117854

Keyword

nonn

Author

Robert G. Wilson v, May 01 2006

Status

approved