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A014689
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a(n) = prime(n)-n, the number of nonprimes less than prime(n).
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64
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1, 1, 2, 3, 6, 7, 10, 11, 14, 19, 20, 25, 28, 29, 32, 37, 42, 43, 48, 51, 52, 57, 60, 65, 72, 75, 76, 79, 80, 83, 96, 99, 104, 105, 114, 115, 120, 125, 128, 133, 138, 139, 148, 149, 152, 153, 164, 175, 178, 179, 182, 187, 188, 197, 202, 207, 212, 213, 218, 221, 222
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OFFSET
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1,3
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COMMENTS
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a(n) = A000040(n) - n. a(n) = inverse (frequency distribution) sequence of A073425(n), i.e., number of terms of sequence A073425(n) less than n. a(n) = A065890(n) + 1, for n >= 1. a(n) - 1 = A065890(n) = the number of composite numbers, i.e., (A002808) less than n-th primes, (i.e., < A000040(n)). - Jaroslav Krizek, Jun 27 2009
Conjecture: Each residue class contains infinitely many terms of this sequence. Similarly, for any integers m > 0 and r, we have prime(n) + n == r (mod m) for infinitely many positive integers n. - Zhi-Wei Sun, Nov 25 2013
First differences are A046933 = differences minus one between successive primes. - Gus Wiseman, Jan 18 2020
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(Haskell)
a014689 n = a000040 n - fromIntegral n
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CROSSREFS
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The sum of prime factors of n is A001414(n).
The sum of prime indices of n is A056239(n).
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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More terms from Vasiliy Danilov (danilovv(AT)usa.net), July 1998
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STATUS
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approved
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