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

1,1

Links

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

Example

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

Mathematica

csp[{a_, b_, c_}]:=If[c-b<b-a, c, a]; Join[{6}, csp/@Partition[Select[Range[ 300], PrimeOmega[#]==2&], 3, 1]] (* Harvey P. Dale, May 06 2014 *)

Prog

(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

Crossrefs

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

Sequence in context: A182164 A294093 A257926 * A357128 A141270 A040032

Adjacent sequences: A116943 A116944 A116945 * A116947 A116948 A116949

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 25 2006

Extensions

Corrected by Harvey P. Dale, May 06 2014

Status

approved