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A252398 Successive n with minimal relative distance |1-theta(n)/n|, where theta(n) = log(A034386(n)) is Chebyshev's theta function. 1
2, 3, 5, 7, 13, 19, 43, 47, 73, 103, 107, 109, 113, 199, 283, 467, 661, 887, 1063, 1069, 1097, 1103, 1109, 1123, 1129, 1303, 1307, 1321, 1327, 1621, 1627, 2803, 3931, 3947, 4273, 4289, 4297, 5867, 5869, 5881, 6373, 6379, 9439, 9473, 9479, 9497, 9551, 9859, 9931, 9949 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first 10000 terms are the same as A108310 (see that sequence for comments). - Charles R Greathouse IV, Dec 18 2014

This sequence, unlike A108310, is presumably infinite; it is finite if and only if theta(n) = n for some number n.

LINKS

Jean-François Alcover and Charles R Greathouse IV, Table of n, a(n) for n = 1..5000 (first 88 terms from Alcover)

Eric Weisstein's MathWorld, Chebyshev functions

Wikipedia, Chebyshev function

EXAMPLE

Given that 1 - theta(3)/3 = 1 - log(6)/3 = 0.40..., 1 - theta(4)/4 = 1 - log(6)/4 = 0.55... and 1 - theta(5)/5 = 1 - log(30)/5 = 0.31..., the next term after 3 is 5.

MATHEMATICA

(* Adapted from PARI *) Reap[For[record = 2; theta = 0; p = 2, p < 2 * 10^8, p = NextPrime[p], theta = theta + Log[p] //N; d = Abs[1 - theta/p]; If[d < record, record = d; Print[p]; Sow[p]]]][[2, 1]]

PROG

(PARI) /* Note: This program may fail if you replace 1e6 with a number larger than 1e17, and will certainly fail at some point below 1e316. These large numbers are not remotely feasible at the moment. */

r=th=0; forprime(p=2, 1e6, th+=log(p); t=th/p; if(t>r, r=t; print1(p", "); if(t>1, warning("theta(n) > n, possible missed terms")))) \\ Charles R Greathouse IV, Dec 17 2014

CROSSREFS

Cf. A016040, A035158, A057872, A083535, A108310, A215013.

Sequence in context: A113864 A188754 A108310 * A330383 A146999 A147485

Adjacent sequences:  A252395 A252396 A252397 * A252399 A252400 A252401

KEYWORD

nonn

AUTHOR

Jean-François Alcover, Dec 17 2014

STATUS

approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)