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 21-24 of 24 results.

A164372 Greater of twin primes (A006512) which are not Labos primes (A080359).

Original entry on oeis.org

5, 7, 151, 229, 571, 643, 1051, 1153, 1669, 1723, 1951, 2029, 2131, 2239, 2311, 2593, 2659, 3001, 3121, 3169, 3253, 3583, 3769, 4003, 4219, 4231, 4483, 4549, 4723, 4789, 5641, 6451, 6553, 6661, 6763, 6949, 6961, 7129, 7351, 8011, 9043, 9463, 9631, 10009
Offset: 1

Views

Author

Vladimir Shevelev, Aug 14 2009

Keywords

Comments

The terms greater than 7 are in A164294.

Links

Crossrefs

Cf. A006512, A080359, A164294, A164371, A104272, A001359.

Programs

  • PARI
    lista(nn)= {my(vlp = readvec("/gp/bfiles/b080359.txt")); forprime (p=3, nn, if (isprime(p-2) && !vecsearch(vlp, p), print1(p, ", ")););} \\ Michel Marcus, Jan 15 2014

Extensions

More terms from Michel Marcus, Jan 15 2014

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.

A195465 The first a(n) n-gap primes are lessers of twin primes, a(n) maximal.

Original entry on oeis.org

0, 5, 5, 17, 5, 6, 14, 6, 24, 75, 2, 4, 27, 11, 48, 50, 46, 9, 21, 7, 16, 137, 4, 55, 85, 14, 111, 24, 102, 291, 67, 89, 155, 180, 137, 330, 127, 413, 250, 241, 332, 619, 139, 234, 453, 929, 94, 160, 169, 22, 131, 434
Offset: 1

Views

Author

Vladimir Shevelev, Sep 19 2011

Keywords

Comments

For definition of n-gap primes, see comment to A195270.
Conjecture: a(n)>0 for n>1. This conjecture is equivalent to the conjecture that all terms of A195325 are lessers of twin primes.

Crossrefs

Cf. A195325, A080192, A195270, A195271, A164368, A194658, A164294.

Programs

  • Maple
    a:= proc(n) local i, p, q;
      p, q:= 2, 3;
      for i from 0 do
        while nextprime(n*p) < (n*q) do
          p, q:= q, nextprime(q)
        od;
        if not isprime(p+2) then return i fi;
        p, q:= q, nextprime(q)
      od
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Sep 20 2011
  • Mathematica
    a[n_] := a[n] = Module[{i, p = 2, q = 3}, For[i = 0, True, i++, While[NextPrime[n p] < n q, p = q; q = NextPrime[q]]; If[!PrimeQ[p+2], Return[i]]; p = q; q = NextPrime[q]]];
Array[a, 20] (* Jean-François Alcover, Nov 21 2020, after Alois P. Heinz *)

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 21-24 of 24 results.

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