A116946 Closest semiprime to n-th semiprime S that is different from S (break ties by taking the smaller semiprime).

6, 4, 10, 9, 15, 14, 22, 21, 26, 25, 34, 33, 34, 39, 38, 49, 51, 49, 57, 58, 57, 65, 62, 65, 77, 74, 85, 86, 85, 86, 93, 94, 93, 94, 111, 115, 118, 119, 118, 122, 121, 122, 133, 134, 133, 142, 141, 142, 146, 145, 158, 159, 158, 159, 169, 166, 178, 177, 185

Offset: 1

Author

Jonathan Vos Post, Mar 25 2006

Keywords

• easy
• nonn

Examples

			Closest semiprimes to 4, 6, 9, 10, 14, 15, 21 are 6, 4, 10, 9, 15, 14, 22.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358 (semiprimes), A051701 (analog for primes).

Programs

Mathematica

csp[{a_,b_,c_}]:=If[c-bHarvey P. Dale, May 06 2014 *)

Python

from sympy import factorint
def semiprime(n): return sum(e for e in factorint(n).values()) == 2
def nextsemiprime(n):
  nxt = n + 1
  while not semiprime(nxt): nxt += 1
  return nxt
def aupton(terms):
  prv, cur, nxt, alst = 0, 4, 6, []
  while len(alst) < terms:
    alst.append(prv if 2*cur - prv <= nxt else nxt)
    prv, cur, nxt = cur, nxt, nextsemiprime(nxt)
  return alst
print(aupton(59)) # Michael S. Branicky, Jun 04 2021

Extensions

Corrected by Harvey P. Dale, May 06 2014