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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
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, #]<DivisorSigma[ 1, #+1]&]] (* Harvey P. Dale, Apr 30 2011 *)
PROG
(Haskell)
a053230 n = a053230_list !! (n-1)
a053230_list = zipWith (-) (tail a053224_list) a053224_list
-- Reinhard Zumkeller, May 07 2012
(PARI) last=ls=1; for(n=2, 200, ns=sigma(n+1); if(ls>=ns, ls=ns; next); ls=ns; print1(n-last", "); last=n) \\ Charles R Greathouse IV, Mar 09 2014
CROSSREFS
Sequence in context: A279759 A185714 A168353 * A194334 A242259 A048766
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.)