A256485 -id:A256485 - cp's OEIS frontend

A256475 Numbers n for which there are more primes in range [prime(n)^2, prime(n)prime(n+1)] than in range [prime(n)prime(n+1), prime(n+1)^2].

13, 25, 26, 38, 39, 41, 42, 43, 44, 45, 48, 49, 50, 55, 58, 59, 61, 63, 65, 69, 73, 74, 77, 81, 86, 88, 92, 96, 98, 101, 103, 106, 107, 108, 109, 116, 117, 120, 121, 122, 124, 125, 128, 141, 142, 143, 145, 146, 148, 149, 151, 155, 158, 159, 166, 169, 172, 173, 177, 179, 181, 182, 183, 190, 191, 194, 195, 196, 197, 206

Offset: 1

Antti Karttunen, Mar 30 2015

nonn

Positions of negative terms in A256470.

Equally: Numbers n for which there are less primes in range [prime(n)*prime(n+1), prime(n+1)^2] than in range [prime(n)^2, prime(n)*prime(n+1)].

Antti Karttunen, Table of n, a(n) for n = 1..3084

Complement: A256474.
Setwise difference of A256477 and A256471.
Cf. A256485 (corresponding primes).
Cf. A256470.

Select[Range@210, Count[Range[Prime[#]^2, Prime[#] Prime[# + 1]], ?PrimeQ] > Count[Range[Prime[#] Prime[# + 1], Prime[# + 1]^2], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

A256484 Primes p for which there are at least as many primes in the range [pnextprime(p), nextprime(p)^2] as in the range [p^2, pnextprime(p)], where nextprime(p) gives the next prime after prime p.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 199, 211, 233, 239, 241, 251, 263, 269, 281, 293, 311, 317, 331, 337, 349, 353, 359, 379, 383, 397, 401, 409, 421, 431, 433, 439, 449, 461, 463, 467, 487, 491, 499, 509

Offset: 1

Antti Karttunen, Mar 30 2015

nonn

			For p=3, we have in the range [3*3, 3*5] two primes, {11, 13}, and in the latter range [3*5, 5*5] we have three primes {17, 19, 23}, thus 3 is included in the sequence.

Antti Karttunen, Table of n, a(n) for n = 1..3457

Complement among primes: A256485.
Cf. A256472 (a subsequence).
Cf. A000040, A256474.

Select[Prime@ Range@ 100, Count[Range[# NextPrime[#], NextPrime[#]^2], ?PrimeQ] >= Count[Range[#^2, # NextPrime[#]], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

(define (A256484 n) (A000040 (A256474 n)))

a(n) = A000040(A256474(n)).

cp's OEIS Frontend

A256475 Numbers n for which there are more primes in range [prime(n)^2, prime(n)prime(n+1)] than in range [prime(n)prime(n+1), prime(n+1)^2].

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A256484 Primes p for which there are at least as many primes in the range [pnextprime(p), nextprime(p)^2] as in the range [p^2, pnextprime(p)], where nextprime(p) gives the next prime after prime p.

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cp's OEIS Frontend

A256475 Numbers n for which there are more primes in range [prime(n)^2, prime(n)*prime(n+1)] than in range [prime(n)*prime(n+1), prime(n+1)^2].

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Mathematica

A256484 Primes p for which there are at least as many primes in the range [p*nextprime(p), nextprime(p)^2] as in the range [p^2, p*nextprime(p)], where nextprime(p) gives the next prime after prime p.

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A256475 Numbers n for which there are more primes in range [prime(n)^2, prime(n)prime(n+1)] than in range [prime(n)prime(n+1), prime(n+1)^2].

A256484 Primes p for which there are at least as many primes in the range [pnextprime(p), nextprime(p)^2] as in the range [p^2, pnextprime(p)], where nextprime(p) gives the next prime after prime p.