A120044
The 10^n-th 3-almost prime.
Original entry on oeis.org
8, 45, 412, 3918, 38991, 395085, 4046429, 41657362, 429891626, 4439956573, 45851698382, 473238120286, 4880292241955, 50280826966354
Offset: 0
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ThreeAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j)] - j + 1, {i, PrimePi[n^(1/3)]}, {j, i, PrimePi@ Sqrt[n/Prime@i]}]; ThreeAlmostPrime[n_] := Block[{e = Floor[Log[2, n]], a, b}, a = 2^e; Do[b = 2^p; While[ThreeAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Do[ Print@ThreeAlmostPrime[10^n], {n, 0, 13}]
ThreePrime[n_] := Block[{e = Floor[ Log[2, n] +2], a, b}, a = 2^e; Do[b = 2^p; While[ ThreePrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Table[ ThreePrime[n], {n, 0, 13}]
A120045
The (10^n)-th 4-almost prime.
Original entry on oeis.org
16, 88, 693, 5958, 54328, 511725, 4922511, 47997635, 472514554, 4683086217, 46636297326, 466032880556
Offset: 0
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FourAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}];
FourAlmostPrime[n_] := Block[{e = Floor[Log[2, n] +3], a, b}, a = 2^e; Do[b = 2^p; While[FourAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Do[ Print@FourAlmostPrime[10^n], {n, 0, 11}]
A120046
The 10^n-th 5-almost prime.
Original entry on oeis.org
32, 176, 1272, 10374, 89896, 810220, 7475818, 70185558, 667561977, 6411296283, 62037096770, 603813941738
Offset: 0
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FiveAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k*Prime@l)] - l + 1, {i, PrimePi[n^(1/5)]}, {j, i, PrimePi[(n/Prime@i)^(1/4)]}, {k, j, PrimePi[(n/(Prime@i*Prime@j)^(1/3))]}, {l, k, PrimePi@Sqrt[(n/(Prime@i*Prime@j*Prime@k))]}];
FiveAlmostPrime[n_] := Block[{e = Floor[Log[2, n] +4], a, b}, a = 2^e; Do[b = 2^p; While[FiveAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Do[ Print@FiveAlmostPrime[10^n], {n, 0, 13}]
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lista(nmax) = {my(pow = 1, c = 0, n = 0); for(k = 1, oo, if(bigomega(k) == 5, c++; if(c == pow, print1(k, ", "); if(n == nmax, break); pow *= 10; n++)));} \\ Amiram Eldar, Apr 29 2024
a(6) corrected and a(7)-a(9) added by
Amiram Eldar, Apr 29 2024
A131867
a(n) is the 2^n-th semiprime.
Original entry on oeis.org
4, 6, 10, 22, 46, 93, 202, 407, 849, 1774, 3693, 7671, 15999, 33146, 68703, 142682, 295003, 610757, 1261573, 2603453, 5369633, 11058907, 22758881, 46796443, 96132103, 197329777, 404737537, 829538129, 1698995201, 3477431507, 7113030933, 14540737711
Offset: 0
a(0)=4 is the first semiprime;
a(1)=6 is the 2nd semiprime;
a(16)=295003 is the 65536th semiprime.
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SP( n=0 /*tested number*/,c=0 /*count of semiprimes*/, step=2)={ local( l=c+!c ); /* negative/positive step means arithmetic/geometric progression of output threshold l */ until( 0, until(l<=c++,until(bigomega(n+=1)==2,));print1(/*c ":" */ n ", "); if(step>0,l*=step,l-=step))}
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use ntheory ":all"; my($i,$g)=(0,0); forsemiprimes { print $g++," $\n" if ++$i == 1<<$g; } 10**8; # _Dana Jacobsen, Sep 10 2018
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use ntheory ":all"; print "$ ",nth_semiprime(1<<$),"\n" for 0..40; # Dana Jacobsen, Oct 08 2018
A117324
Prime(10^n) modulo semiprime(10^n).
Original entry on oeis.org
2, 3, 227, 729, 22965, 380555, 156346, 10920166, 202913258, 2973399074, 39284376410, 489544827463, 5874954672992
Offset: 0
prime(10^0) modulo semiprime(10^0) = 2 mod 4 = 2.
prime(10^1) modulo semiprime(10^1) = 29 mod 26 = 3.
prime(10^2) modulo semiprime(10^2) = 541 mod 314 = 227.
Showing 1-5 of 5 results.
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