A046024
a(n) = smallest k such that Sum_{ i = 1..k } 1/prime(i) exceeds n.
Original entry on oeis.org
1, 3, 59, 361139, 43922730588128390
Offset: 0
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) <= n, m++];
m, {n, 0, 4}] (* Robert Price, Mar 27 2019 *)
-
a(n)=my(t); forprime(p=2,, t+=1./p; if(t>n, return(primepi(p)))) \\ Charles R Greathouse IV, Apr 29 2015
a(4) found by Tomás Oliveira e Silva (tos(AT)det.ua.pt), using the fourth term of
A016088. - Dec 14 2005
A103600
Smallest prime p such that Sum_{primes q <= p} 1/q >= n/6.
Original entry on oeis.org
2, 2, 2, 3, 3, 5, 7, 13, 29, 53, 109, 277, 809, 2741, 11789, 64663, 483281, 5195977, 85861889, 2358926351, 118185163069, 12041724518809
Offset: 1
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/6, m++];
Prime[m], {n, 1, 17}] (* Robert Price, Mar 27 2019 *)
a(1), a(2), a(4) added for correctness, and a(19-21) included by
Martin Raab, Mar 31 2009
A103592
a(n) is the smallest prime p such that Sum_{primes q <= p} 1/q >= n/2.
Original entry on oeis.org
2, 5, 29, 277, 11789, 5195977, 118185163069, 1801241230056600523
Offset: 1
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/2, m++];
Prime[m], {n, 1, 8}] (* Robert Price, Mar 27 2019 *)
A103599
Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/6.
Original entry on oeis.org
1, 1, 1, 2, 2, 3, 4, 6, 10, 16, 29, 59, 140, 400, 1413, 6467, 40261, 361139, 4990906, 114916199, 4833601540
Offset: 1
-
For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/6, Print[k]; Break[]]]] (* Robert Price, Dec 09 2013 *)
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/6, m++];
m, {n, 1, 17}] (* Robert Price, Mar 27 2019 *)
a(2)-a(4) and a(19)-a(21) added by
Robert Price, Dec 10 2013
A103593
Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/3.
Original entry on oeis.org
1, 2, 3, 6, 16, 59, 400, 6467, 361139, 114916199
Offset: 1
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];
m, {n, 1, 10}] (* Robert Price, Mar 27 2019 *)
A103594
Smallest prime p such that Sum_{primes q <= p} 1/q >= n/3.
Original entry on oeis.org
2, 3, 5, 13, 53, 277, 2741, 64663, 5195977, 2358926351, 12041724518809, 1801241230056600523
Offset: 1
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];
Prime[m], {n, 1, 10}] (* Robert Price, Mar 27 2019 *)
A103595
Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/4.
Original entry on oeis.org
1, 1, 2, 3, 5, 10, 21, 59, 231, 1413, 15474, 361139, 22347214, 4833601540
Offset: 1
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/4, m++];
m, {n, 1, 14}] (* Robert Price, Mar 27 2019 *)
A103596
Smallest prime p such that Sum_{primes q <= p} 1/q >= n/4.
Original entry on oeis.org
2, 2, 3, 5, 11, 29, 73, 277, 1453, 11789, 169751, 5195977, 420055319, 118185163069
Offset: 1
-
For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/4, Print[Prime[k]]; Break[]]]]
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/4, m++];
Prime[m], {n, 1, 14}] (* Robert Price, Mar 27 2019 *)
A103597
Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/5.
Original entry on oeis.org
1, 1, 2, 2, 3, 5, 7, 13, 25, 59, 170, 644, 3402, 27178, 361139, 8947437, 474314304
Offset: 1
-
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/5, m++];
m, {n, 1, 17}] (* Robert Price, Mar 27 2019 *)
A103598
Smallest prime p such that Sum_{primes q <= p} 1/q >= n/5.
Original entry on oeis.org
2, 2, 3, 3, 5, 11, 17, 41, 97, 277, 1013, 4789, 31627, 314723, 5195977, 159490147, 10443979657
Offset: 1
-
For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/5, Print[Prime[k]]; Break[]]]]
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/5, m++];
Prime[m], {n, 1, 17}] (* Robert Price, Mar 27 2019 *)
Showing 1-10 of 10 results.
Comments