The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A064777 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A064777

Numbers k such that prime(k) - pi(k) is divisible by k.
(history; published version)

#23 by Susanna Cuyler at Tue Jun 15 08:06:01 EDT 2021

STATUS

proposed

approved

#22 by Michel Marcus at Tue Jun 15 01:38:56 EDT 2021

STATUS

editing

proposed

#21 by Michel Marcus at Tue Jun 15 01:38:51 EDT 2021

PROG

(PARI) isok(k) = ((prime(k) - primepi(k)) % k) == 0; \\ Michel Marcus, Jun 15 2021

CROSSREFS

Cf. A000040, A000720, A065139, A111181.

STATUS

proposed

editing

#20 by Joerg Arndt at Tue Jun 15 01:34:12 EDT 2021

STATUS

editing

proposed

#19 by Joerg Arndt at Tue Jun 15 01:33:52 EDT 2021

EXAMPLE

k = 18 is a term: prime(18) = 61. , pi(18) = 7. , and (61-7)/18 = 54/18 = 3.

#18 by Joerg Arndt at Tue Jun 15 01:32:54 EDT 2021

NAME

Difference between Numbers k such that prime(nk) and - pi(nk) is divisible by nk.

FORMULA

Solutions to (PrimePi(x) - prime(x)) mod x = (A000040(x) - A000720(x)) mod x = 0.

EXAMPLE

n k = 18: prime(18) = 61. pi(18) = 7. (61-7)/18 = 3.

n = 273585: prime(273585) = 3854117. pi(273585) = 23927.

(3854117-23927)/273585 = 14.

n = 1735537: prime(1735537) = 27899177. pi(1735537) = 130585.

(27899177-130585)/1735537 = 16.

STATUS

proposed

editing

#17 by Jon E. Schoenfield at Tue Jun 15 00:19:21 EDT 2021

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Tue Jun 15 00:18:43 EDT 2021

FORMULA

Solutions to Mod[(PrimePi[(x]) -Prime[ prime(x], )) mod x] = Mod[(A000040[(x]) - A000720[(x], )) mod x] = 0.

STATUS

proposed

editing

#15 by Michel Marcus at Mon Jun 14 10:37:55 EDT 2021

STATUS

editing

proposed

#14 by Michel Marcus at Mon Jun 14 10:37:47 EDT 2021

FORMULA

Solutions to Mod[PrimPiPrimePi[x]-Prime[x], x] = Mod[A000040[x]-A000720[x], x] = 0.

STATUS

approved

editing

Discussion

Mon Jun 14

10:37

Michel Marcus: typo