cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Mar 30 2015

Keywords

Comments

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).

Links

Crossrefs

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.

Programs

Formula

a(n) = A256469(n) - A256468(n).
a(n) = 3 - A256449(n).

A256471 Numbers n for which there is an equal number of primes in range [prime(n)^2, prime(n)*prime(n+1)] as there are primes in range [prime(n)*prime(n+1), prime(n+1)^2].

Original entry on oeis.org

1, 10, 14, 17, 20, 90, 110, 152, 176, 185, 193, 230, 344, 377, 391, 392, 404, 441, 442, 542, 1066, 1533, 1550, 1632, 1638, 1639, 1810, 2115, 2210, 2302, 2567, 2768, 2921, 3172, 3518, 3615, 3764, 4357, 4577, 4787, 4853, 5060, 5278, 6329
Offset: 1

Views

Author

Antti Karttunen, Mar 30 2015

Keywords

Crossrefs

Positions of zeros in A256470.
Cf. A256472, A256473 (the corresponding primes).

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.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Mar 30 2015

Keywords

Examples

			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.

Crossrefs

Cf. A000040, A065091, A256471, A256472.

Programs

Formula

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

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.

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

Views

Author

Antti Karttunen, Mar 30 2015

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

Formula

a(n) = A000040(A256474(n)).
Showing 1-4 of 4 results.

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