A256476 -id:A256476 - cp's OEIS frontend

A256470 a(n) = A256469(n) - A256468(n).

0, 1, 2, 3, 1, 6, 1, 3, 3, 0, 3, 2, -2, 0, 4, 6, 0, 4, 4, 0, 2, 3, 10, 13, -1, -2, 3, 4, 4, 34, 5, 3, 5, 17, 6, 2, 8, -2, -6, 3, -4, -4, -3, -2, -1, 9, 25, -2, -6, -4, 12, 4, 6, 9, -6, 18, 1, -2, -11, 7, -8, 27, -10, 3, -1, 12, 11, 13, -3, 5, 3, 5, -13, -8, 10, 16, -4, 14, 3, 12, -3, 23, 5, 4, 6, -8, 19, -13, 1, 0

Offset: 1

Antti Karttunen, Mar 30 2015

sign

a(n) = Difference between the number of primes occurring in range [prime(n)*prime(n+1), prime(n+1)^2] and the number of primes occurring in range [prime(n)^2, prime(n)*prime(n+1)].

In other words, a(n) tells how many more primes there are in the latter part of the range prime(n)^2 .. prime(n+1)^2 (after the geometric mean of its limits), than in its first part (before the geometric mean of its limits).

Antti Karttunen, Table of n, a(n) for n = 1..6541
A. Karttunen, Sequences A256470 and A050216 compared with OEIS Plot2-script (See also the ratio-plots linked in A256468.)

Positions of zeros: A256471. Cf. also A256472, A256473.
Positions of nonnegative terms: A256474, negative terms: A256475.
Positions of strictly positive terms: A256476, terms less than or equal to zero: A256477.
Cf. A256449, A256468, A256469.

(define (A256470 n) (- (A256469 n) (A256468 n)))

a(n) = A256469(n) - A256468(n).

a(n) = 3 - A256449(n).

A256474 Numbers n for which there are at least as many primes in the range [prime(n)prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)prime(n+1)].

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 46, 47, 51, 52, 53, 54, 56, 57, 60, 62, 64, 66, 67, 68, 70, 71, 72, 75, 76, 78, 79, 80, 82, 83, 84, 85, 87, 89, 90, 91, 93, 94, 95, 97, 99, 100

Offset: 1

Antti Karttunen, Mar 30 2015

nonn

Positions of nonnegative terms in A256470.

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

Complement: A256475.
Union of A256471 and A256476.
Cf. A256484 (corresponding primes).
Cf. A256470.

Select[Range@100, Count[Range[Prime[#] Prime[# + 1], Prime[# + 1]^2], ?PrimeQ] >= Count[Range[Prime[#]^2, Prime[#] Prime[# + 1]], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

A256477 Numbers n for which the number of primes in the range [prime(n)prime(n+1), prime(n+1)^2] is less than or equal to the number of primes in the range [prime(n)^2, prime(n)prime(n+1)].

Original entry on oeis.org

1, 10, 13, 14, 17, 20, 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, 90, 92, 96, 98, 101, 103, 106, 107, 108, 109, 110, 116, 117, 120, 121, 122, 124, 125, 128, 141, 142, 143, 145, 146, 148, 149, 151, 152, 155, 158, 159, 166, 169

Offset: 1

Antti Karttunen, Mar 30 2015

nonn

Positions where A256470 is zero or negative.

Antti Karttunen, Table of n, a(n) for n = 1..3128

Complement: A256476.
Union of A256471 and A256475.
Cf. A256470.

Select[Range@ 170, Count[Range[Prime[#] Prime[# + 1], Prime[# + 1]^2], ?PrimeQ] <= Count[Range[Prime[#]^2, Prime[#] Prime[# + 1]], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

cp's OEIS Frontend

A256470 a(n) = A256469(n) - A256468(n).

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A256474 Numbers n for which there are at least as many primes in the range [prime(n)prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)prime(n+1)].

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Mathematica

A256477 Numbers n for which the number of primes in the range [prime(n)prime(n+1), prime(n+1)^2] is less than or equal to the number of primes in the range [prime(n)^2, prime(n)prime(n+1)].

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cp's OEIS Frontend

A256470 a(n) = A256469(n) - A256468(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A256474 Numbers n for which there are at least as many primes in the range [prime(n)*prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)*prime(n+1)].

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A256477 Numbers n for which the number of primes in the range [prime(n)*prime(n+1), prime(n+1)^2] is less than or equal to the number of primes in the range [prime(n)^2, prime(n)*prime(n+1)].

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A256474 Numbers n for which there are at least as many primes in the range [prime(n)prime(n+1), prime(n+1)^2] as in the range [prime(n)^2, prime(n)prime(n+1)].

A256477 Numbers n for which the number of primes in the range [prime(n)prime(n+1), prime(n+1)^2] is less than or equal to the number of primes in the range [prime(n)^2, prime(n)prime(n+1)].