A084141 - OEIS

A084141

a(n) is the index in sequence A084138 when the value of that sequence is one (1), i.e., there is exactly one case where there are exactly a(n) primes between m and 2m, exclusively, for m > 0.

0, 22, 36, 47, 79, 98, 114, 134, 173, 178, 184, 210, 218, 221, 245, 254, 262, 284, 297, 305, 327, 333, 373, 387, 396, 426, 459, 466, 470, 484, 530, 544, 563, 567, 575, 587, 616, 650, 694, 700, 706, 708, 737, 776, 859, 881, 885, 898, 926, 939, 974, 993, 1002

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

This calculation relies on the fact that Pi(2*m) - Pi(m) > m/(3*log(m)) for m >= 5. Conjecture: There are an infinite number of terms in this sequence.

REFERENCES

P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 140.

LINKS

Table of n, a(n) for n=0..52.

Eric Weisstein's World of Mathematics, Bertrand's Postulate.

EXAMPLE

a(3)=47 because the 3rd one in sequence A084138 is its item 47. There is exactly one case where there are exactly 47 primes between m and 2m.

CROSSREFS

Cf. A060715, A060756, A084138, A084139, A084140, A084142.

Sequence in context: A061561 A233404 A167277 * A259736 A082261 A335373

Adjacent sequences: A084138 A084139 A084140 * A084142 A084143 A084144

KEYWORD

nonn

AUTHOR

Harry J. Smith, May 15 2003

STATUS

approved