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 1-5 of 5 results.

A140791 First occurrence of prime gap 10*n.

Original entry on oeis.org

139, 887, 4297, 19333, 31907, 43331, 173359, 542603, 404851, 396733, 1468277, 1895359, 5518687, 7621259, 13626257, 33803689, 27915737, 17051707, 142414669, 378043979, 20831323, 47326693, 607010093, 391995431, 387096133, 944192807
Offset: 1

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Author

Lekraj Beedassy, Jul 14 2008

Keywords

References

  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 139, pp 47, Ellipses, Paris 2008.

Crossrefs

Formula

a(n)=A000230(5n), a(3n) = A224522(n) = A058193(5n). - M. F. Hasler, Apr 09 2013

Extensions

Offset corrected by Arkadiusz Wesolowski, Jun 07 2011

A204672 Primes followed by a gap of 120.

Original entry on oeis.org

1895359, 2898239, 6085441, 7160227, 7784039, 7803491, 7826899, 8367397, 8648557, 9452959, 10052071, 10863973, 11630503, 11962823, 12109697, 12230233, 12415681, 14411737, 14531899, 15014557, 15020737, 15611909, 16179041
Offset: 1

Views

Author

M. F. Hasler, Jan 18 2012

Keywords

Crossrefs

Cf. A058193 (first gap of 6n), A140791 (first gap of 10n).
Cf. A126771 (gap 60), A126724 (gap 150), A204673 (gap 180).

Programs

  • MATLAB
    N = 2*10^7; % to get all terms <= N
    P = primes(N+120);
    J = find(P(2:end) - P(1:end-1) == 120);
    P(J)  % Robert Israel, Feb 28 2017
  • Mathematica
    Transpose[Select[Partition[Prime[Range[1100000]],2,1],Last[#]-First[#] == 120&]] [[1]] (* Harvey P. Dale, Jul 11 2014 *)
  • PARI
    g=120;c=o=0;forprime(p=1,default(primelimit),(-o+o=p)==g&write("c:/temp/b204672.txt",c++" "p-g))
    

A224472 Primes followed by a gap of 300.

Original entry on oeis.org

4758958741, 5612345261, 6169169561, 6306815239, 6646984159, 7335508261, 8645089003, 8806019249, 9047808247, 9148138313, 9466071347, 9907846261, 10055451683, 11063821453, 11475026363, 11603081459, 12292390637, 12750876857, 13833827471, 14636472007, 15876700949
Offset: 1

Views

Author

Zak Seidov, Apr 07 2013

Keywords

Comments

The first twin gap equal to 300 occurs for p = 6537587646371. - Giovanni Resta, Apr 07 2013

Crossrefs

Cf. A058193 (first gap of 6n), A140791 (first gap of 10n), A126771 (gap 60), A126724 (gap 150), A204673 (gap 180), A204807 (gap 200), A000230, A001359, A204672, A029710, A031924-A031938, A061779, A098974, A124594-A124596, A126784, A134116-A134124, A204665-A204670.

A267721 a(n) is the least term of A030461 with gap = 6*n between consecutive primes or 0 if no such term exists.

Original entry on oeis.org

3137, 199211, 523541, 16691693, 1393313963, 2428124317, 3498135023, 7318973237, 4028940343, 191353191413, 221327221393, 507217507289, 937253937331, 10402271040311, 843911844001, 25654632565559, 81661078166209, 55778515577959, 82237498223863
Offset: 1

Views

Author

Jean-Marc Rebert, Jan 20 2016

Keywords

Comments

Subsequence of A030461.
a(n) is the concatenation of the smallest prime p and the next prime q, such that p + 6n = q and the concatenations of these 2 primes is also prime. a(n) = 0 if no such term exists.

Examples

			a(1) = A030461(2) = 3137. gap =  37 - 31 = 6 = 6 * 1.
a(2) = 199211, because 199211 is the first term in A030461, with gap = 211 - 199 = 12 = 6 * 2.
		

Crossrefs

Programs

  • Maple
    Primes:= select(isprime,[seq(i,i=3..10^7,2)]):
    cati:= (x,y) -> 10^(1+ilog10(y))*x+y;
    for i from 1 to nops(Primes)-1 do
      g:= Primes[i+1]-Primes[i];
      if g mod 6 <> 0 then next fi;
      if assigned(A[g/6]) then next fi;
      z:= cati(Primes[i],Primes[i+1]);
      if isprime(z) then A[g/6]:= z fi;
    od:
    seq(A[i],i=1..max(map(op,[indices(A)]))); # Robert Israel, Jan 24 2016

A224522 Least prime which is followed by a gap of 30n.

Original entry on oeis.org

4297, 43331, 404851, 1895359, 13626257, 17051707, 20831323, 391995431, 1391048047, 4758958741, 6291356009, 20068818197, 53241805651, 82490815123, 63816175447, 482423533897, 2209016910131, 738832927927, 4442109925217, 4872634110067, 12644461143649, 10653514291843, 15712145060693, 111113196467011
Offset: 1

Views

Author

M. F. Hasler, Apr 09 2013

Keywords

Comments

Data up to 2e9 computed independently and (up to 391995431) double-checked with A140791. Data beyond 2e9 taken from Nicely's web page (which would yield further terms, at least up to a(47) - notice that the "?" in column 10, e.g. for gap 1440, indicates that the listed values is the first *known*, but maybe not the first occurrence). See there for credits.

Programs

  • PARI
    o=2;g=30;forprime(p=3,,(o+g != o=p) & next; print1(p-g",");g+=30) \\ Warning: this code assumes that the sequence is increasing, which may not be the case. - M. F. Hasler, Apr 09 2013

Formula

a(n) = A000230(15n) = A058193(5n) = A140791(3n)
Showing 1-5 of 5 results.