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A066883
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Number of primes in the interval [p(n),p(n)^2] minus p(n), where p(n) is the n-th prime.
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3
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0, 0, 2, 5, 15, 21, 38, 46, 68, 108, 121, 171, 210, 227, 268, 341, 412, 441, 524, 585, 612, 711, 781, 888, 1042, 1126, 1165, 1247, 1286, 1381, 1720, 1814, 1972, 2018, 2306, 2361, 2536, 2715, 2838, 3029, 3217, 3290, 3635, 3709, 3848, 3920, 4370, 4836
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Haga's conjecture (see link below) is that if the integers from 1 to p^2 (p prime) are put in a p by p square in standard order, then there's a transversal consisting of primes; i.e. a set of p primes containing exactly one number in each row and column. E.g. for p=5 the primes 5, 7, 11, 19, 23 work. Since p is needed for the p-th column, primes less than p can't be used. a(n) is the number of primes available minus the number needed for the transversal.
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REFERENCES
| Paulo Ribenboim, The New Book of Prime Number Records, 3rd ed., 1995, Springer, pp. 397-398
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
Carlos Rivera, The prime puzzles & problems connection, conjecture 26
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FORMULA
| a(n) = A054272(n)-A000040(n).
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MATHEMATICA
| a[n_] := PrimePi[(p=Prime[n])^2]-PrimePi[p-1]-p
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PROG
| (BASIC) 20 for Y=1 to 140 30 A=nxtprm(A):B=A^2 40 for X=A to B 50 if X=prmdiv(X) then C=C+1 60 next X 70 print A; C; C-A; "-"; 80 C=0 90 next Y
(PARI) { for (n=1, 1000, a=primepi((p=prime(n))^2) - primepi(p - 1) - p; write("b066883.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 04 2010]
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CROSSREFS
| Cf. A066885, A066886, A054272.
Sequence in context: A058221 A146122 A146121 * A146120 A104585 A146119
Adjacent sequences: A066880 A066881 A066882 * A066884 A066885 A066886
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KEYWORD
| easy,nonn
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AUTHOR
| Enoch Haga (Enokh(AT)comcast.net), Jan 26 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 08 2002
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