

A000101


Increasing gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps).
(Formerly M2485 N0984)


32



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
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OFFSET

1,1


COMMENTS

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, SpringerVerlag, see p. 133.
H. Cramer, On the order of magnitude of the difference between consecutive prime numbers, Acta Arith. 2 (1936), 396403.
T. Oliveira e Silva, S. Herzog, S. Pardi, Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4 × 10^18, Math. Comp. 83 (2014), 20332060.
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 and M. F. Hasler, Table of n, a(n) for n = 1..75
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
Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao, Long gaps between primes, arXiv:1412.5029
Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.
Thomas R. Nicely, Home Page
Tomás Oliveira e Silva, Computational projects
D. Shanks, On maximal gaps between successive primes, Math. Comp., 18 (1964), 646651.
Marek Wolf, A Note on the Andrica Conjecture, arXiv:1010.3945.
J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221224.
Index entries for primes, gaps between


FORMULA

a(n) = A002386(n) + A005250(n) = A008995(n1) + 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 (* JeanFrançois Alcover, Mar 31 2011 *)


PROG

(PARI) p=q=2; g=0; until( g<(q=nextprime(1+p=q))p & print1(p+g=qp, ", "), ) \\  M. F. Hasler, Dec 13 2007


CROSSREFS

Cf. A001223 (differences between primes), A002386 (lower ends), A005250 (record gaps), A107578.
Cf. A005669, A111943.
Sequence in context: A168607 A057735 A095302 * A253899 A037152 A084748
Adjacent sequences: A000098 A000099 A000100 * A000102 A000103 A000104


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

See A002386 for complete list of known terms and further references.


STATUS

approved



