A114058
Start of record gap in even semiprimes (A100484).
Original entry on oeis.org
4, 6, 14, 46, 178, 226, 1046, 1774, 2258, 2654, 19102, 31366, 39218, 62794, 311842, 721306, 740522, 984226, 2699066, 2714402, 4021466, 9304706, 34103414, 41662646, 94653386, 244329494, 379391318, 383825566, 774192266
Offset: 1
gap[a(1)] = A100484(2)-A100484(1) = 6 - 4 = 2.
gap[a(2)] = A100484(3)-A100484(2) = 10 - 6 = 4.
gap[a(3)] = A100484(5)-A100484(4) = 22 - 14 = 8.
gap[a(4)] = A100484(10)-A100484(9) = 58 - 46 = 12.
gap[a(5)] = A100484(25)-A100484(24) = 194 - 178 = 16.
gap[a(6)] = A100484(31)-A100484(30) = 254 - 226 = 28.
-
f[n_] := Block[{k = n + 2}, While[ Plus @@ Last /@ FactorInteger@k != 2, k += 2]; k]; lst = {}; d = 0; a = b = 4; Do[{a, b} = {b, f[a]}; If[b - a > d, d = b - a; AppendTo[lst, a]], {n, 10^8}]; lst (* Robert G. Wilson v *)
A114417
Records in 7-almost prime gaps, ordered by merit.
Original entry on oeis.org
64, 96, 112, 168, 210, 280
Offset: 1
Records defined in terms of A114407 and A046308:
n A114407(n) A114407(n)/log(A046308(n))
1 64 64/log 128 = 30.371914
2 96 96/log 192 = 42.0443868
3 32 32/log 288 = 13.0113433
4 112 112/log 320 = 44.7079021
5 16 16/log 432 = 6.07099172
6 32 32/log 448 = 12.0696509
7 168 168/log 480 = 62.6575474
8 24 24/log 648 = 8.53614076
A114418
Records in 8-almost prime gaps ordered by merit.
Original entry on oeis.org
128, 192, 224, 336, 420, 560
Offset: 1
Records defined in terms of A114408 and A046310:
n A114418(n) A114418(n)/log(A046310(n)).
1 128 128/log 256 = 53.1508495
2 192 192/log 384 = 74.2938824
3 64 64/log 576 = 23.1848568
4 224 224/log 640 = 79.8238182
5 32 32/log 864 = 10.8972758
6 64 64/log 896 = 21.6779549
7 336 336/log 960 = 112.665809
8 48 48/log 1296 = 15.4211665
22 420 420/log 2496 = 123.629603
A114413
Records in 3-almost prime gaps ordered by merit.
Original entry on oeis.org
4, 6, 12, 58, 83
Offset: 1
Records defined in terms of A114403 and A014612:
n A114403(n) A114403(n)/log_10(A014612(n))
= ========== =============================
1 4 4/log_10(8) = 4.42923746
2 6 6/log_10(12) = 5.55977045
3 2 2/log_10(18) = 1.59327954
4 7 7/log_10(20) = 5.38035251
5 1 1/log_10(27) = 0.698634425
6 2 2/log_10(28) = 1.38201907
7 12 12/log_10(30) = 8.12390991
...
19 14 14/log_10(78) = 7.3992072
A114416
Records in 6-almost prime gaps ordered by merit.
Original entry on oeis.org
32, 48, 56, 84, 105, 140
Offset: 1
Records defined in terms of A114406 and A046306:
n A114406(n) A114406(n)/log(A046306(n)).
1 32 32/log 64 = 17.7169498
2 48 48/log 96 = 24.2146479
3 16 16/log 144 = 7.41302726
4 56 56/log 160 = 25.4069653
5 8 8/log 216 = 3.42692589
6 16 16/log 224 = 6.80779215
7 84 84/log 240 = 35.2909853
8 12 12/log 324 = 4.77983862
...
22 105 105/log 624 = 37.5646032
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