OFFSET
1,1
COMMENTS
It seems that the expansion consists of only {1,2,3,4}.
The first exception is a(18360922) = 6, corresponding to the gap from 36721680 to 36721686. - 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.
MAPLE
with(numtheory): f := [seq( `if`((sigma(i) > sigma(i+1)), 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 22 2011 *)
Differences[Flatten[Position[Partition[DivisorSigma[1, Range[300]], 2, 1], _?(#[[1]]>#[[2]]&), 1, Heads->False]]] (* Harvey P. Dale, Oct 18 2020 *)
PROG
(Haskell)
a053238 n = a053238_list !! (n-1)
a053238_list = zipWith (-) (tail a053226_list) a053226_list
-- Reinhard Zumkeller, Oct 16 2011
(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
KEYWORD
nonn,nice
AUTHOR
Asher Auel, Jan 10 2000
STATUS
approved