cp's OEIS Frontend

A066883 Number of primes in the interval [p(n), p(n)^2] minus p(n), where p(n) is the n-th prime.

%I A066883 #14 Dec 24 2015 23:54:55
%S A066883 0,0,2,5,15,21,38,46,68,108,121,171,210,227,268,341,412,441,524,585,
%T A066883 612,711,781,888,1042,1126,1165,1247,1286,1381,1720,1814,1972,2018,
%U A066883 2306,2361,2536,2715,2838,3029,3217,3290,3635,3709,3848,3920,4370,4836
%N A066883 Number of primes in the interval [p(n), p(n)^2] minus p(n), where p(n) is the n-th prime.
%C A066883 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.
%D A066883 Paulo Ribenboim, The New Book of Prime Number Records, 3rd ed., 1995, Springer, pp. 397-398
%H A066883 Harry J. Smith, <a href="/A066883/b066883.txt">Table of n, a(n) for n = 1..1000</a>
%H A066883 Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_026.htm">The prime puzzles & problems connection, conjecture 26</a>
%F A066883 a(n) = A054272(n)-A000040(n).
%t A066883 a[n_] := PrimePi[(p=Prime[n])^2]-PrimePi[p-1]-p
%o A066883 (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
%o A066883 (PARI) { for (n=1, 1000, a=primepi((p=prime(n))^2) - primepi(p - 1) - p; write("b066883.txt", n, " ", a) ) } \\ _Harry J. Smith_, Apr 04 2010
%Y A066883 Cf. A066885, A066886, A054272.
%K A066883 easy,nonn
%O A066883 1,3
%A A066883 _Enoch Haga_, Jan 26 2002
%E A066883 Edited by _Dean Hickerson_, Jun 08 2002