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A111181
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Prime(x) - Pi(x).
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0
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2, 2, 3, 5, 8, 10, 13, 15, 19, 25, 26, 32, 35, 37, 41, 47, 52, 54, 59, 63, 65, 71, 74, 80, 88, 92, 94, 98, 99, 103, 116, 120, 126, 128, 138, 140, 145, 151, 155, 161, 166, 168, 177, 179, 183, 185, 196, 208, 212, 214, 218, 224, 225, 235, 241, 247, 253, 255, 260, 264
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OFFSET
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1,1
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COMMENTS
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Conjecture: There will always be an x such that a(x+1) - a(x) = k for k=1,2.. However, x becomes large when k > 70.
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LINKS
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Table of n, a(n) for n=1..60.
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FORMULA
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Prime(x) = the x-th prime. Pi(x) = number of primes <= x
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MATHEMATICA
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Table[Prime[n]-PrimePi[n], {n, 60}] (* From Harvey P. Dale, Mar 11 2012 *)
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PROG
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(PARI) primexmpix(n, k) = { local(x, y, z); for(x=1, n, y=prime(x)-primepi(x); z=prime(x+1)-primepi(x+1); if(z-y == k, print1(y", ") ) ) }
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CROSSREFS
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Sequence in context: A199962 A114990 A157176 * A076777 A111123 A179523
Adjacent sequences: A111178 A111179 A111180 * A111182 A111183 A111184
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 22 2005
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STATUS
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approved
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