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A057820 First differences of sequence of consecutive prime powers (A000961). 20
1, 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, 6, 2, 3, 3, 4, 2, 6, 2, 2, 6, 8, 4, 2, 4, 2, 4, 8, 4, 2, 1, 3, 6, 2, 10, 2, 6, 6, 4, 2, 4, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 2, 8, 5, 1, 6, 6, 2, 6, 4, 2, 6, 4, 14, 4, 2, 4, 14, 6, 6, 4, 2, 4, 6, 2, 6, 6, 6, 4, 6, 8, 4, 8, 10, 2, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
a(n) = 1 iff A000961(n) = A006549(k) for some k. - Reinhard Zumkeller, Aug 25 2002
Also run lengths of distinct terms in A070198. - Reinhard Zumkeller, Mar 01 2012
LINKS
FORMULA
a(n) = A000961(n+1) - A000961(n).
EXAMPLE
Odd differences arise in pairs in neighborhoods of powers of 2, like {..,2039,2048,2053,..} gives {..,11,5,..}
MAPLE
A057820 := proc(n)
A000961(n+1)-A000961(n) ;
end proc: # R. J. Mathar, Sep 23 2016
MATHEMATICA
Map[Length, Split[Table[Apply[LCM, Range[n]], {n, 1, 150}]]] (* Geoffrey Critzer, May 29 2015 *)
Join[{1}, Differences[Select[Range[500], PrimePowerQ]]] (* Harvey P. Dale, Apr 21 2022 *)
PROG
(PARI) isA000961(n) = (omega(n) == 1 || n == 1)
n_prev=1; for(n=2, 500, if(isA000961(n), print(n-n_prev); n_prev=n)) \\ Michael B. Porter, Oct 30 2009
(Haskell)
a057820_list = zipWith (-) (tail a000961_list) a000961_list
-- Reinhard Zumkeller, Mar 01 2012
CROSSREFS
Sequence in context: A205028 A325055 A325526 * A054012 A062083 A133114
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 08 2000
EXTENSIONS
Offset corrected and b-file adjusted by Reinhard Zumkeller, Mar 03 2012
STATUS
approved

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Last modified May 29 10:17 EDT 2024. Contains 372926 sequences. (Running on oeis4.)