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 A000101 Increasing gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps). (Formerly M2485 N0984) 34
 3, 5, 11, 29, 97, 127, 541, 907, 1151, 1361, 9587, 15727, 19661, 31469, 156007, 360749, 370373, 492227, 1349651, 1357333, 2010881, 4652507, 17051887, 20831533, 47326913, 122164969, 189695893, 191913031, 387096383, 436273291, 1294268779 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A002386 for complete list of known terms and further references. Except for a(1)=3 and a(2)=5, a(n) = A168421(k). Primes 3 and 5 are special in that they are the only primes which do not have a Ramanujan prime between them and their double, <= 6 and 10 respectively. Because of the large size of a gap, there are many repeats of the prime number in A168421. - John W. Nicholson, Dec 10 2013 REFERENCES B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 133. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS John W. Nicholson, Table of n, a(n) for n = 1..77 (terms 1..75 from Alex Beveridge and M. F. Hasler) Jens Kruse Andersen, Maximal Prime Gaps Alex Beveridge, Table giving known values of A000101(n), A005250(n), A107578(n) Andrew Booker, The Nth Prime Page H. Cramer, On the order of magnitude of the difference between consecutive prime numbers, Acta Arith. 2 (1936), 396-403. T. Oliveira e Silva, Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18, Math. Comp., 83 (2014), 2033-2060. Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao, Long gaps between primes, arXiv:1412.5029 [math.NT], 2014-2016. Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053 [math.NT], 2013. Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019. Thomas R. Nicely, Home Page Tomás Oliveira e Silva, Computational projects D. Shanks, On maximal gaps between successive primes, Math. Comp., 18 (1964), 646-651. Robert G. Wilson v, Notes (no date) Marek Wolf, A Note on the Andrica Conjecture, arXiv:1010.3945 [math.NT], 2010. J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224. FORMULA a(n) = A002386(n) + A005250(n) = A008995(n-1) + 1. - M. F. Hasler, Dec 13 2007 MATHEMATICA s = {3}; gm = 1; Do[p = Prime[n + 1]; g = p - Prime[n]; If[g > gm, Print[p]; AppendTo[s, p]; gm = g], {n, 2, 1000000}]; s  (* Jean-François Alcover, Mar 31 2011 *) PROG (PARI) p=q=2; g=0; until( g<(q=nextprime(1+p=q))-p & print1(p+g=q-p, ", "), ) \\ M. F. Hasler, Dec 13 2007 CROSSREFS Cf. A001223 (differences between primes), A002386 (lower ends), A005250 (record gaps), A107578, A290000. Cf. A005669, A111943. Sequence in context: A168607 A057735 A095302 * A253899 A037152 A084748 Adjacent sequences:  A000098 A000099 A000100 * A000102 A000103 A000104 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified March 19 20:29 EDT 2019. Contains 321332 sequences. (Running on oeis4.)