

A210210


Least number k among 1, ..., n such that pi(p+2*n)  pi(p+n) = pi(p+n)  pi(p) > 0 with p = prime(k), or 0 if such a number k does not exist, where pi(.) is given by A000720.


1



0, 1, 2, 4, 2, 2, 4, 1, 2, 3, 3, 6, 2, 9, 4, 6, 7, 4, 4, 6, 3, 3, 3, 5, 2, 6, 4, 4, 4, 8, 3, 4, 6, 3, 3, 8, 8, 6, 6, 7, 7, 10, 7, 6, 14, 5, 5, 8, 5, 4, 6, 3, 3, 13, 2, 14, 12, 12, 12, 18, 18, 18, 11, 11, 11, 17, 10, 11, 11, 16, 16, 9, 9, 16, 15, 16, 8, 14, 14, 14
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OFFSET

1,3


COMMENTS

Conjecture: a(n) > 0 for all n > 1.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..5000


EXAMPLE

a(4) = 4 since prime(4) = 7 with pi(7+2*4)  pi(7+4) = pi(7+4)  pi(7) = 1 > 0, but pi(2+2*4)  pi(2+4) = 1 < pi(2+4)  pi(2) = 2, pi(3+2*4)  pi(3+4) = 1 < pi(3+4)  pi(3) = 2, and pi(5+2*4)  pi(5+4) = 2 > pi(5+4)  pi(5) = 1.


MATHEMATICA

p[k_, n_]:=Prime[k]+n>=Prime[k+1]&&k+PrimePi[Prime[k]+2n]==2*PrimePi[Prime[k]+n]
Do[Do[If[p[k, n], Print[n, " ", k]; Goto[aa]], {k, 1, n}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 80}]


CROSSREFS

Cf. A000040, A000720, A238281.
Sequence in context: A183193 A331470 A021809 * A117007 A213433 A294354
Adjacent sequences: A210207 A210208 A210209 * A210211 A210212 A210213


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 24 2014


STATUS

approved



