A185008 Next semiprime after 10*n.

4, 14, 21, 33, 46, 51, 62, 74, 82, 91, 106, 111, 121, 133, 141, 155, 161, 177, 183, 194, 201, 213, 221, 235, 247, 253, 262, 274, 287, 291, 301, 314, 321, 334, 341, 355, 361, 371, 381, 391, 403, 411, 422, 437, 445, 451, 466, 471, 481, 493, 501, 511, 526, 533

Offset

0,1

Comments

This is to semiprimes A001358 as A218255 is to primes A000040.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n) = MIN[k in A218255 and k > 10*n].

Example

a(0) = 4 because 4=2^2 is the least semiprime > 10*0=0.
a(1) = 14 because 14=2*7 is the least semiprime > 10*1=10.

Mathematica

SemiprimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; NextSemiprime[n_] := Module[{m = n + 1}, While[! SemiPrimeQ[m], m++]; m]; Table[NextSemiprime[10*n], {n, 0, 100}] (* T. D. Noe, Nov 02 2012 *)
nsp[n_]:=Module[{k=n+1}, While[PrimeOmega[k]!=2, k++]; k]; Table[nsp[10n], {n, 0, 60}] (* Harvey P. Dale, Mar 17 2023 *)

Prog

(Python)
from sympy.ntheory.factor_ import primeomega
def nextsemiprime(n):
  while primeomega(n + 1) != 2: n += 1
  return n + 1
def a(n): return nextsemiprime(10*n)
print([a(n) for n in range(54)]) # Michael S. Branicky, Apr 14 2021

Crossrefs

Cf. A001358, A218255.

Sequence in context: A326004 A297358 A267768 * A165721 A197638 A051806

Adjacent sequences: A185005 A185006 A185007 * A185009 A185010 A185011

Keyword

nonn,easy

Author

Jonathan Vos Post, Nov 01 2012

Status

approved