A259758 Squarefree semiprimes of the form (2*p - 3) * (3*p - 2), p prime.

21, 91, 209, 589, 851, 2881, 7739, 10541, 16171, 26069, 29329, 75151, 95129, 110839, 165169, 194219, 216409, 220991, 264389, 374749, 411601, 653069, 717949, 829931, 1108969, 1119311, 1171741, 1269139, 1416689, 2059789, 3161729, 3374249, 3428459, 4924109

Offset: 1

Author

Reinhard Zumkeller, Jul 05 2015

Keywords

• nonn

Comments

a(n) = (2*A259730(n) - 3) * (3*A259730(n) - 2);

3431 = A033569(24) = (2*25-3)*(3*25-2) = 47*73 = A006881(946) is the smallest term in the intersection of A006881 and A033569 not belonging to this sequence.

Examples

			.    n | p = A259730(n) | 2*p - 3 | 3*p - 2 |   a(n)
.  ----+----------------+---------+---------+--------
.    1 |              3 |       3 |       7 |     21
.    2 |              5 |       7 |      13 |     91
.    3 |              7 |      11 |      19 |    209
.    4 |             11 |      19 |      31 |    589
.    5 |             13 |      23 |      37 |    851
.    6 |             23 |      43 |      67 |   2881
.    7 |             37 |      71 |     109 |   7739
.    8 |             43 |      83 |     127 |  10541
.    9 |             53 |     103 |     157 |  16171
.   10 |             67 |     131 |     199 |  26069
.   11 |             71 |     139 |     211 |  29329
.   12 |            113 |     223 |     337 |  75151  .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A259730, subsequence of A006881, subsequence of A033569.

Programs

Haskell

a259758 n = (2 * p - 3) * (3 * p - 2)  where p = a259730 n

Mathematica

Select[Table[(2p-3)(3p-2),{p,Prime[Range[200]]}],PrimeOmega[#]==2&&SquareFreeQ[ #]&] (* Harvey P. Dale, Jul 20 2022 *)

Formula

a(n) = 6*A259730(n)^2 - 13*A259730(n) + 6.