Original entry on oeis.org
4, 15, 34, 249, 391, 565, 771, 886, 1915, 3814, 5149, 5739, 6046, 7354, 9169, 10765, 11611, 15814, 16321, 18429, 20665, 22426, 24259, 28141, 29499, 32311, 36769, 39106, 43161, 48291, 52786, 53709, 57481, 60394, 63379, 65409, 67471, 69565
Offset: 1
a(27) = 4*97^2 - 9*97 + 6 = 36769 = 83 * 443.
a(28) = 4*100^2 - 9*100 + 6 = 39106 = 2 * 19553.
a(27) and a(28) are horizontally adjacent in the prime spiral, hence part of a clump and not isolated semiprimes as in A113688.
a(45) = 4*157^2 - 9*157 + 6 = 97189 = 17 * 5717 is the greatest member under 10^5.
-
IsSemiprime:= func; [s: n in [2..150] | IsSemiprime(s) where s is 4*n^2 - 9*n + 6]; // Vincenzo Librandi, Sep 22 2012
-
Select[Table[4 n^2 - 9 n + 6, {n, 140}], PrimeOmega[#] == 2 &] (* Vincenzo Librandi, Sep 22 2012 *)
Original entry on oeis.org
86, 298, 371, 1243, 1541, 2426, 2627, 3053, 4258, 5366, 5663, 6281, 6602, 6931, 7613, 8327, 9073, 9458, 10661, 13283, 14702, 15191, 16706, 18293, 18838, 23486, 25361, 26002, 26651, 27973, 28646, 34318, 35063, 36577, 38123, 41311, 43786, 44627
Offset: 1
a(10) = 4*37^2 - 3*37 + 1 = 5366 = 2 * 2683.
a(11) = 4*38^2 - 3*38 + 1 = 5663 = 7 * 809.
a(10) and a(11) are horizontally adjacent in the prime spiral, hence part of a clump and not isolated semiprimes as in A113688.
a(57) = 4*156^2 - 3*156 + 1 = 96877 = 11 * 8807 is the greatest member under 10^5.
-
IsSemiprime:= func; [s: n in [1..120] | IsSemiprime(s) where s is 4*n^2 - 3*n + 1]; // Vincenzo Librandi, Sep 22 2012
-
Select[Table[4*n^2 - 3*n + 1, {n, 150}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)
Original entry on oeis.org
6, 69, 106, 265, 334, 411, 589, 799, 1041, 1174, 1315, 1959, 2329, 3394, 4659, 5221, 5815, 7099, 8146, 8511, 10869, 16449, 21979, 23181, 23794, 25681, 26326, 31774, 33949, 35439, 36961, 38515, 40101, 43369, 45051, 48511, 50289, 52099, 54874
Offset: 1
a(4) = 4*9^2 - 7*9 + 4 = 265 = 5 * 53.
a(5) = 4*10^2 - 7*10 + 4 = 334 = 2 * 167.
a(6) = 4*11^2 - 7*11 + 4 = 411 = 3 * 137.
a(4), a(5) and a(6) are horizontally adjacent in the semiprime spiral, hence part of a clump and not isolated semiprimes as in A113688. a(9), a(10) and a(11) are another such horizontal string of 3 adjacent semiprimes.
a(46) = 4*151^2 - 7*151 + 4 = 90151 = 17 * 5303 is the greatest member under 10^5 (it is coincidence that this integer ends, base 10, with the same 151 that is the index of the quadratic).
-
IsSemiprime:= func; [s: n in [2..120] | IsSemiprime(s) where s is 4*n^2 - 7*n + 4]; // Vincenzo Librandi, Sep 22 2012
-
Select[Table[4*n^2 - 7*n + 4, {n, 200}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)
Showing 1-3 of 3 results.
Comments