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A002386
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Primes (lower end) with record gaps to the next consecutive prime: primes p(k) where p(k+1) - p(k) exceeds p(j+1) - p(j) for all j < k.
(Formerly M0858 N0327)
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122
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2, 3, 7, 23, 89, 113, 523, 887, 1129, 1327, 9551, 15683, 19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201, 2010733, 4652353, 17051707, 20831323, 47326693, 122164747, 189695659, 191912783, 387096133, 436273009, 1294268491
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 133.
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, Sect 6.1, Table 1.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 14.
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).
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LINKS
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FORMULA
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MATHEMATICA
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s = {2}; gm = 1; Do[p = Prime[n]; g = Prime[n + 1] - p; If[g > gm, Print[p]; AppendTo[s, p]; gm = g], {n, 2, 1000000}]; s (* Jean-François Alcover, Mar 31 2011 *)
Module[{nn=10^7, pr, df}, pr=Prime[Range[nn]]; df=Differences[pr]; DeleteDuplicates[ Thread[ {Most[ pr], df}], GreaterEqual[#1[[2]], #2[[2]]]&]][[All, 1]] (* The program generates the first 26 terms of the sequence. *) (* Harvey P. Dale, Sep 24 2022 *)
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PROG
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(PARI) a(n)=local(p, g); if(n<2, 2*(n>0), p=a(n-1); g=nextprime(p+1)-p; while(p=nextprime(p+1), if(nextprime(p+1)-p>g, break)); p) /* Michael Somos, Feb 07 2004 */
(PARI) p=q=2; g=0; until( g<(q=nextprime(1+p=q))-p && print1(q-g=q-p, ", "), ) \\ M. F. Hasler, Dec 13 2007
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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