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 11-17 of 17 results.

A182366 Records in A194217.

Original entry on oeis.org

8, 10, 24, 36, 60, 64, 84, 114, 124, 144, 202, 226, 228
Offset: 1

Views

Author

Vladimir Shevelev, Apr 26 2012

Keywords

Comments

Records in A194217(n) occur at n = 2, 4, 10, 14, 43, 95, 145, 167, 287, 415, 560, 635, 982,...

Crossrefs

Cf. A104272, A080359, A193507, A194184, A194186, A194217.

A194217 a(n) = A104272(n)-A080359(n).

Original entry on oeis.org

0, 8, 4, 10, 10, 4, 6, 6, 0, 24, 0, 4, 18, 36, 12, 10, 6, 0, 36, 36, 34, 0, 0, 12, 0, 10, 24, 18, 34, 0, 14, 0, 22, 0, 0, 10, 0, 0, 18, 24, 0, 4, 60, 48, 10, 0, 0, 0, 0, 28, 24, 0, 0, 0, 16, 36, 36, 6, 8, 12, 36, 10, 0, 0, 24, 0, 22, 54, 30, 0, 14, 12, 18, 22
Offset: 1

Views

Author

Vladimir Shevelev, Aug 18 2011

Keywords

Comments

Conjecture: Asymptotic density of nonzero terms is 3/4.

Links

Crossrefs

Cf. A104272, A080359, A193507, A194184, A194186.

Programs

  • Mathematica
    nn = 100;
R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s+1]] = k], {k, Prime[3nn]}
];
A104272 = R = R + 1;
T = Table[0, {nn + 1}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s <= nn && T[[s+1]] == 0, T[[s+1]] = k], {k, Prime[3nn]}
];
A080359 = Rest[T];
A104272 - A080359 (* Jean-François Alcover, Aug 19 2018, after T. D. Noe *)

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

A182391 Numbers n for which A104272(n) = A080359(n).

Original entry on oeis.org

1, 9, 11, 18, 22, 23, 25, 30, 32, 34, 35, 37, 38, 41, 46, 47, 48, 49, 52, 53, 54, 63, 64, 66, 70, 75, 76, 79, 80, 82, 84, 94, 98, 99, 101, 102, 105, 108, 109, 110, 113, 114, 115, 124, 127, 128, 131, 135, 136, 139, 140, 148, 149, 150, 151, 154, 156, 158, 160
Offset: 1

Views

Author

Vladimir Shevelev, Apr 27 2012

Keywords

Comments

Number m is in the sequence iff 1) there exists only composite number k such that 2*k-1 is prime and A060715(k)=m; 2) there is no prime p such that 2*p-1 is prime and A060715(p)=m-1.

Crossrefs

Cf. A104272, A080359, A164554, A193507, A194184, A194186, A194217, A182366.

Formula

A194217(n)=0.

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.

A182392 Numbers n for which there exists only composite number k such that A060715(k) = n and 2*k-1 is prime, but A104272(n) differs from A080359(n).

Original entry on oeis.org

3, 8, 36, 55, 58, 83, 129, 134, 143, 155, 186, 197, 207, 218, 269, 295, 309, 310, 361, 362, 380, 396, 412, 454, 466, 473, 505, 511, 514, 544, 549, 556, 563, 616, 631, 660, 666, 677, 683, 697, 771, 781, 788, 797, 812, 873, 874, 881, 883, 894, 906, 953
Offset: 1

Views

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 27 2012

Keywords

Comments

There exists a prime p=p(n) such that 2*p-1 is prime and A060715(p)=a(n)-1 (cf. comment in A182391).

Crossrefs

Cf. A104272, A080359, A164554, A193507, A194184, A194186, A194217, A182366, A182391.
Previous Showing 11-17 of 17 results.

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