A256473 - OEIS

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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.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..44.

FORMULA

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

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.

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 *)

PROG

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

CROSSREFS

Cf. A000040, A065091, A256471, A256472.

Sequence in context: A177104 A078330 A107210 * A119739 A163579 A290401

Adjacent sequences: A256470 A256471 A256472 * A256474 A256475 A256476

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 30 2015

STATUS

approved