This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
With n = 4, a(4)=42, and A202186(4) = 8. So, A190874(42)=8. However, A174641(A202186(4)-1) = A174641(8-1) = A168425(a(4)) = A168425(42) = 509.
With n = 4, A202187(4)=42, and a(4) = 8. So, A190874(42)=8. However, A174641(a(4)-1) = A174641(8-1) = A168425(A202187(4)) = A168425(42) = 509.
perl -Mntheory=:all -nE 'my $n = $1 if /(\d+)$/; say ++$x," ",prev_prime($n) unless $seen{$n}++;' b174641.txt # Dana Jacobsen, Jul 14 2016
use ntheory ":all"; my($max,$r)=(0,ramanujan_primes(1e7)); for (0..$#$r-1) { my $d=prime_count($r->[$+1])-prime_count($r->[$]); if ($d > $max) { say $r->[$]; $max=$d; } } # _Dana Jacobsen, Jul 14 2016
For n=10, the n-th Ramanujan prime is A104272(n)= 97, the value of k = 25, so i is >= 26, i-n >= 16, the i-n prime is 53, and 2*53 = 106. This leaves the range [97, 106] for the 26th prime which is 101. In this example, 53 is the small associated Ramanujan prime.
nn = 100;
t = Table[0, {nn}];
Do[m = PrimePi[2n] - PrimePi[n]; If[0 < m <= nn, t[[m]] = n], {n, 15 nn}];
A084139 = Join[{1}, t];
a[n_] := NextPrime[A084139[[n]]];
Array[a, nn] (* Jean-François Alcover, Nov 07 2018, after T. D. Noe in A084139 *)
use ntheory ":all"; say next_prime((nth_ramanujan_prime($)+1) >> 1) for 1..100; # _Dana Jacobsen, Mar 02 2016
For n=10, the n-th Ramanujan prime is A104272(n)= 97, the value of k = 25, so i is >= 26, i-n >= 16, the i-n prime is 53, and 2*53 = 106. This leaves the range [97, 106] for the 26th prime which is 101. In this example, 101 is the large associated Ramanujan prime.
nn = 100; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--];
If[s < nn, R[[s+1]] = k], {k, Prime[3 nn]}
];
RamanujanPrimes = R + 1;
Prime[PrimePi[#]+1]& /@ RamanujanPrimes (* Jean-François Alcover, Nov 03 2018, after T. D. Noe in A104272 *)
genit(n=100)={my(L=vector(n),s=0,k=1,z);for(k=1,prime(3*n)-1,if(ispseudoprime(k),s++);if(k%2==0&&ispseudoprime(k/2),s--);if(snextprime(x+1),L);v} \\ Bill McEachen, Jun 24 2023 (incorporates code from A104272)
use ntheory ":all"; say next_prime(nth_ramanujan_prime($)) for 1..100; # _Dana Jacobsen, Dec 25 2015
A168421(19) = 127, A104272(19) = 227; so a(19) = 2*A168421(19) - A104272(19) = 254 - 227 = 27. Note: for n = 20, 21, 22, 23, A168421(n) = 127. Because A168421 remains the same for these n and A104272 increases, the size of the range for a(n) for these n decreases. Note: a(18) = 2*97 - 181 = 194 - 181 = 13. This is nearly half a(19). The actual gap betweens A104272(19) and the next prime, 229, is 2.
nn = 100; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k], {k, Prime[3 nn]}];
A104272 = R + 1; t = Table[0, {nn}];
Do[m = PrimePi[2 n] - PrimePi[n]; If[0 < m <= nn, t[[m]] = n], {n, 15 nn}];
A168421 = NextPrime[Join[{1}, t]] // Most;
A165979 = 2 A168421 - A104272 (* Jean-François Alcover, Nov 07 2018, after T. D. Noe in A104272 *)
67 and 71 are the first two Ramanujan primes that are consecutive primes, so a(2) = 67.
nn=10000; t=Table[0, {nn}]; len=Prime[3*nn]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s
use ntheory ":all"; my $r=ramanujan_primes(1e8); my $max = 0; for (0..$#$r-2) { my $k=0; $k++ while next_prime($r->[$+$k]) == $r->[$+$k+1]; say ++$max," ",$r->[$] while $k >= $max; } # _Dana Jacobsen, Jul 14 2016
a(17) = eta(17) = 3. Or, R_3 = 17.
nn = 100; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k], {k, Prime[3 nn]}];
A104272 = R + 1;
Table[Boole[MemberQ[A104272, k]], {k, 1, 100}] // Accumulate (* Jean-François Alcover, Nov 07 2018, using T. D. Noe's code for A104272 *)
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