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 A174602 Smallest prime that begins a run of n Ramanujan primes that are consecutive primes. 6
 2, 67, 227, 227, 227, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 562871, 793487, 809707, 809707, 984241, 984241, 984241, 6234619, 11652013, 41662651, 41662651, 41662651, 94653397, 383825567, 869730887, 953913871, 953913871, 953913871 (list; graph; refs; listen; history; text; internal format)
 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[\$_+\$k]) == \$r->[\$_+\$k+1]; say ++\$max, " ", \$r->[\$_] while \$k >= \$max; } # Dana Jacobsen, Jul 14 2016 CROSSREFS Cf. A104272 (Ramanujan primes), A174641 (runs of non-Ramanujan primes). Sequence in context: A217599 A107214 A371509 * A154880 A160958 A046848 Adjacent sequences: A174599 A174600 A174601 * A174603 A174604 A174605 KEYWORD nonn AUTHOR T. D. Noe, Nov 29 2010 STATUS approved

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Last modified September 9 04:58 EDT 2024. Contains 375759 sequences. (Running on oeis4.)