A084141 a(n) is the index in sequence A084138 when the value of that sequence is 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

Offset

1,2

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=1..53.

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

Extensions

Offset changed by Sean A. Irvine, Mar 13 2026

Status

approved