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 A053230 First differences between numbers k for which sigma(k) < sigma(k+1). 10
 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS It seems that the expansion consists of only {1,2,3,4}. The first exception is a(10010491) = 6, corresponding to the gap from 20021153 to 20021159. - Charles R Greathouse IV, Mar 09 2014 The asymptotic mean of this sequence is 2 (Erdős, 1936). - Amiram Eldar, Mar 19 2021 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Paul Erdős, On a problem of Chowla and some related problems, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; alternative link. FORMULA a(n) = A053224(n+1) - A053224(n). MAPLE with(numtheory): f := [seq( `if`((sigma(i+1) > sigma(i)), i, print( )), i=1..5000)]; seq( f[i+1] - f[i], i=1..2000); MATHEMATICA Differences[Select[Range[250], DivisorSigma[1, #]=ns, ls=ns; next); ls=ns; print1(n-last", "); last=n) \\ Charles R Greathouse IV, Mar 09 2014 CROSSREFS Cf. A000203, A053224, A053231, A053232, A053233, A053234, A053235, A053236, A053237, A053238. Sequence in context: A279759 A185714 A168353 * A194334 A242259 A048766 Adjacent sequences: A053227 A053228 A053229 * A053231 A053232 A053233 KEYWORD nonn,nice AUTHOR Asher Auel, Jan 10 2000 STATUS approved

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Last modified February 21 15:08 EST 2024. Contains 370236 sequences. (Running on oeis4.)