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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 Michael B. Porter, Table of n, a(n) for n = 1..10000 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 Cf. A000961, A036616, A001223. Sequence in context: A205028 A325055 A325526 * A054012 A062083 A133114 Adjacent sequences: A057817 A057818 A057819 * A057821 A057822 A057823 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.)