A254325
Sequence of semiprimes with all cumulating sums being semiprime.
Original entry on oeis.org
4, 6, 15, 26, 55, 111, 237, 469, 926, 1858, 3711, 7419, 14849, 29693, 59435, 118821, 237722, 475378, 950738, 1901474, 3802967, 7605921, 15211942, 30423869, 60847667, 121695326, 243390743, 486781401, 973562795, 1947125641, 3894251303, 7788502531, 15577005118
Offset: 1
4+6=10=2*5, 10+15=25=5*5, 25+26=51=3*17.
-
s={4};a=4;Do[m=a+1;While[2!=PrimeOmega[m]||2!=PrimeOmega[m+a],m++]; AppendTo[s,m];a=m+a,{50}];s
-
{s=[4];a=4;
for(k=1,50,m=a+1while(2<>bigomega(m)||2<>bigomega(m+a),m++);
s=concat(s, m);a=m+a);s}
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
Comments