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A000101 Record gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps).
(Formerly M2485 N0984)
78
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
Alex Beveridge, M. F. Hasler, and John W. Nicholson, Table of n, a(n) for n = 1..80 [Added data from Thomas R. Nicely site. - John W. Nicholson, Oct 27 2021]
Jens Kruse Andersen, Maximal Prime Gaps
Andrew Booker, The Nth Prime Page
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, First occurrence prime gaps [Local copy, pdf only]
Tomás Oliveira e Silva, Computational projects
D. Shanks, On maximal gaps between successive primes, Math. Comp., 18 (1964), 646-651.
Eric Weisstein's World of Mathematics, Prime Gaps
Wikipedia, Prime gap
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. A000040, A001223 (differences between primes), A002386 (lower ends), A005250 (record gaps), A107578.
Cf. also A005669, A111943.
Sequence in context: A057735 A095302 A335367 * A253899 A037152 A084748
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)