OFFSET
1,1
COMMENTS
The first run of 13 consecutive Ramanujan primes was mentioned by Sondow.
Starting at index m = A191228(a(n)) in A190874(m), the first instance of a count of n - 1 consecutive 1's is seen. - John W. Nicholson, Dec 15 2011
LINKS
Dana Jacobsen, Table of n, a(n) for n = 1..42
J. Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-2010.
J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly, 116 (2009) 630-635.
J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011.
J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2.
EXAMPLE
67 and 71 are the first two Ramanujan primes that are consecutive primes, so a(2) = 67.
MATHEMATICA
nn=10000; t=Table[0, {nn}]; len=Prime[3*nn]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s<nn, t[[s+1]]=k], {k, len}]; t=t+1; ind=PrimePi[t]; d=Differences[ind]; cnt=0; n=1; Join[{2}, Reap[Do[If[d[[i]]==1, cnt++; If[cnt==n, Sow[t[[i-n+1]]]; n++], cnt=0], {i, Length[d]}]][[2, 1]]]
PROG
(Perl) 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
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Nov 29 2010
STATUS
approved