The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A256473 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A256473

Odd primes p for which there are exactly as many primes in the range [prevprime(p)^2, prevprime(p)*p] as there are in the range [prevprime(p)*p, p^2], where prevprime(p) gives the previous prime before prime p.
(history; published version)

#11 by N. J. A. Sloane at Tue Mar 31 00:28:22 EDT 2015

STATUS

proposed

approved

#10 by Jon E. Schoenfield at Mon Mar 30 23:00:02 EDT 2015

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Mon Mar 30 23:00:00 EDT 2015

NAME

Odd primes p for which there is an equal number of are exactly as many primes in the range [prevprime(p)^2, prevprime(p)*p] as there are primes in the range [prevprime(p)*p, p^2], where prevprime(p) gives the previous prime before prime p.

STATUS

approved

editing

#8 by N. J. A. Sloane at Mon Mar 30 21:42:11 EDT 2015

STATUS

proposed

approved

#7 by Michael De Vlieger at Mon Mar 30 21:27:21 EDT 2015

STATUS

editing

proposed

#6 by Michael De Vlieger at Mon Mar 30 21:27:18 EDT 2015

MATHEMATICA

Select[Prime@ Range[2, 500], Count[Range[NextPrime[#, -1]^2, # NextPrime[#, -1]], _?PrimeQ] == Count[Range[# NextPrime[#, -1], #^2], _?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

STATUS

proposed

editing

#5 by Antti Karttunen at Mon Mar 30 20:29:25 EDT 2015

STATUS

editing

proposed

#4 by Antti Karttunen at Mon Mar 30 20:29:07 EDT 2015

NAME

Odd primes p for which there is an equal number of primes in range [prevprime(p)^2, prevprime(p)*p] as there are primes in range [prevprime(p)*p, p^2], where prevprime(p) gives the previous prime before prime p.

EXAMPLE

For p=3, we have in the range [2*2, 2*3] just one prime {5}, and also in the latter range [2*3, 3*3] just one prime {7}, thus 3 is included in the sequence.

#3 by Antti Karttunen at Mon Mar 30 20:27:31 EDT 2015

NAME

Odd primes p for which there is exactly the same an equal number of primes in the range [prevprime(p)^2, prevprime(p)*p] than as in the range [prevprime(p)*p, p^2], where prevprime(p) gives the previous prime before prime p.

#2 by Antti Karttunen at Mon Mar 30 15:28:49 EDT 2015

NAME

allocated Odd primes p for Antti Karttunenwhich there is exactly the same number of primes in the range [prevprime(p)^2, prevprime(p)*p] than in the range [prevprime(p)*p, p^2], where prevprime(p) gives the previous prime before prime p.

DATA

3, 31, 47, 61, 73, 467, 607, 883, 1051, 1109, 1181, 1453, 2333, 2593, 2693, 2699, 2789, 3089, 3109, 3919, 8563, 12893, 13009, 13807, 13877, 13879, 15511, 18461, 19483, 20389, 23021, 25087, 26647, 29191, 32803, 33767, 35339, 41651, 43991, 46301, 47051, 49223, 51581, 63127

OFFSET

1,1

FORMULA

a(n) = A065091(A256471(n)) = A000040(1+A256471(n)).

PROG

(Scheme) (define (A256473 n) (A000040 (+ 1 (A256471 n))))

CROSSREFS

Cf. A000040, A065091, A256471, A256472.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Mar 30 2015

STATUS

approved

editing