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.

Previous Showing 21-27 of 27 results.

A195329 Records of A195325.

Original entry on oeis.org

2, 59, 71, 149, 191, 641, 809, 3371, 5849, 9239, 20507, 20981, 32117, 48779, 176777, 191249, 204509, 211061, 223679, 245129, 358877, 654161, 2342771, 3053291, 4297961, 4755347, 6750221, 8019509, 9750371, 10196759, 11237981, 23367077, 34910219, 93929219, 186635747
Offset: 1

Views

Author

Vladimir Shevelev, Sep 15 2011

Keywords

Comments

The sequence is infinite. Conjecture. For n>=2, all terms are in A001359. This conjecture (weaker than the conjecture in comment to A195325) also implies the twin prime conjecture.

Crossrefs

Cf. A195325, A080192, A195270, A195271, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

A195379 3.5-gap primes: Primes prime(k) such that there is no prime between 7*prime(k)/2 and 7*prime(k+1)/2.

Original entry on oeis.org

2, 137, 281, 521, 641, 883, 937, 1087, 1151, 1229, 1277, 1301, 1489, 1567, 1607, 1697, 2027, 2081, 2237, 2381, 2543, 2591, 2657, 2687, 2729, 2801, 2851, 2969, 3119, 3257, 3301, 3359, 3463, 3467, 3529, 3673, 3733, 3793, 3821, 3851, 4073, 4217, 4229, 4241, 4259, 4283, 4337, 4421, 4481
Offset: 1

Views

Author

Vladimir Shevelev, Sep 17 2011

Keywords

Crossrefs

Cf. A080192, A195270, A195271, A195377, A195325, A195329, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

Programs

  • Mathematica
    Select[Prime[Range[1000]], PrimePi[7*NextPrime[#]/2] == PrimePi[7*#/2] &] (* T. D. Noe, Sep 20 2011 *)

Extensions

Corrected by R. J. Mathar, Sep 20 2011

A164920 Primes which are obtained at least by two ways using the iterations of the Bertrand operator (see A164917) beginning with primes of A164368.

Original entry on oeis.org

113, 139, 199, 211, 223, 277, 293, 397, 421, 443
Offset: 1

Views

Author

Vladimir Shevelev, Aug 31 2009

Keywords

Comments

The sequence is connected with our sieve selecting the primes of A164368 from all primes.

Examples

			113 is in the sequence since it is obtained either by iterations of Bertrand operator beginning from 17 (17=>31=>61=>113) or by such iterations beginning with 59 (59=>113), and both of primes 17 and 59 are in A164368.

Links

Crossrefs

Cf. A006992, A164917, A164918, A104272, A164368, A164288.

A164962 a(n) is the least prime from the union {2,3} and A164333, beginning with which the n-th prime p_n is obtained by some number of iterations of the S operator g(see A164960).

Original entry on oeis.org

2, 3, 2, 3, 2, 13, 3, 19, 2, 13, 31, 3, 19, 43, 2, 53, 13, 61, 31, 71, 73, 3, 19, 43, 2, 101, 103, 53, 109, 113, 13, 131, 31
Offset: 1

Views

Author

Vladimir Shevelev, Sep 02 2009

Keywords

Comments

The sequence is connected with our sieve selecting the primes of the union {2,3} and A164333 from all primes. Note that a(n)=n iff p_n is in the considered union, which corresponds to 0's iterations of g.

Links

Crossrefs

Cf. A164333, A055496, A164960, A104272, A080359, A164918, A006992, A164917, A164368, A164288.

A194953 Nonzero values of |A194659(n)-A194186(n+1)|.

Original entry on oeis.org

2, 6, 2, 4, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 6, 2, 2, 4, 2, 2, 10, 6, 6, 2, 2, 2, 6, 2, 8, 8, 4, 6, 4, 2, 8, 4, 8, 4, 4, 6, 4, 2, 4, 2, 4, 2, 2, 22, 2, 2, 6, 4, 4, 8, 2, 2, 10, 2, 2, 2, 2, 4, 4, 4, 2, 2, 2, 2, 2, 10, 2, 2, 8, 18, 2, 2, 4, 4, 2, 12, 6, 6, 8, 20
Offset: 1

Views

Author

Vladimir Shevelev, Sep 06 2011

Keywords

Comments

The sequence (together with A194674) characterizes a right-left symmetry in the distribution of primes over intervals (2*p_n, 2*p_(n+1)), n=1,2,..., where p_n is the n-th prime.

Crossrefs

Cf. A104272, A080359, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

A164966 Primes which are obtained at least by two ways using the iterations of the S operator (see A164960) beginning with primes of the union of {2,3} and A164333.

Original entry on oeis.org

127, 149, 211, 223, 257, 307, 431, 449
Offset: 1

Views

Author

Vladimir Shevelev, Sep 02 2009

Keywords

Comments

The sequence is connected with our sieve selecting the primes of the union of {2,3} and A164333 from all primes.

Links

Crossrefs

Cf. A055496, A164333 A164960, A164962, A164920, A006992, A164917, A164918, A104272, A080359, A164368, A164288.

A166575 Primes p>=5 with the property: if Prime(k)

=Prime(k)+ Prime(k+1).

Original entry on oeis.org

5, 13, 19, 31, 37, 43, 53, 61, 71, 73, 79, 101, 103, 113, 131, 139, 157, 163, 173, 191, 193, 199, 211, 223, 241, 251, 269, 271, 277, 293, 311, 313, 331, 353, 373, 379, 397, 419, 421, 439, 443, 457, 463, 499, 509, 521, 523, 541, 577, 601, 607, 613, 619, 631, 653, 659, 661, 673, 691
Offset: 1

Views

Author

Vladimir Shevelev, Oct 17 2009

Keywords

Comments

If A(x) is the counting function of a(n) not exceeding x, then, in view of the symmetry, it is natural to conjecture that A(x)~pi(x)/2.

Examples

			Let p=13. Then we have 5<13/2<7. Since 13>5+7, then 13 is in the sequence.

Crossrefs

Cf. A166574, A182365, A166307, A166252, A166251, A164368, A104272, A080359, A164333, A164288, A164294, A164554

Programs

  • Mathematica
    Reap[Do[p=Prime[n]; k=PrimePi[p/2]; If[p>=Prime[k]+Prime[k+1], Sow[p]], {n,3,PrimePi[1000]}]][[2,1]]
Previous Showing 21-27 of 27 results.

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