A354448 11-gonal (or hendecagonal) numbers which are products of two distinct primes.

58, 95, 141, 415, 1241, 2101, 2951, 3683, 6031, 7421, 16531, 24383, 35333, 39433, 42001, 50191, 53083, 66551, 83981, 95411, 123421, 146791, 173951, 182911, 190241, 229051, 296321, 307981, 336883, 409361, 442583, 451091, 477101, 500833, 546883, 588431, 669131

Offset

1,1

Comments

A squarefree subsequence of 11-gonal numbers, i.e., numbers of the form k*(9*k-7)/2.

Numbers of the form p*(9*p-7)/2 where p and (9*p-7)/2 are prime, and numbers of the form p*(18*p-7) where p and 18*p-7 are prime. - Robert Israel, Mar 03 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

    58 =  4*(9*4  - 7)/2 =  2*29;
   141 =  6*(9*6  - 7)/2 =  3*47;
   415 = 10*(9*10 - 7)/2 =  5*83;
  3683 = 29*(9*29 - 7)/2 = 29*127.

Maple

N:= 10^6: # for terms <= N
x1:= floor(fsolve(x*(9*x-7)/2=N)[2]):
A:= map(p -> p*(9*p-7)/2, select(p -> isprime(p) and isprime((9*p-7)/2), [seq(i, i=3..x1, 2)])):
x2:= floor(fsolve(x*(18*x-7)=N)[2]):
B:= map(p -> p*(18*p-7), select(p -> isprime(p) and isprime(18*p-7),
  [2, seq(i, i=3..x2, 2)])):
sort([op(A), op(B)]); # Robert Israel, Mar 03 2025

Mathematica

Select[Table[n*(9*n - 7)/2, {n, 1, 400}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* Amiram Eldar, May 30 2022 *)

Prog

(Python)
from sympy import factorint
from itertools import count, islice
def agen():
    for h in (k*(9*k - 7)//2 for k in count(1)):
        f = factorint(h, multiple=True)
        if len(f) == len(set(f)) == 2: yield h
print(list(islice(agen(), 37))) # Michael S. Branicky, May 30 2022

Crossrefs

Intersection of A051682 and A006881.

Sequence in context: A044033 A266451 A124680 * A181462 A260603 A188238

Adjacent sequences: A354445 A354446 A354447 * A354449 A354450 A354451

Keyword

nonn,changed

Author

Massimo Kofler, May 30 2022

Status

approved