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.

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A341550 Primes of the form prime(i)*prime(i+1)+2*prime(i+2).

Original entry on oeis.org

29, 103, 1229, 2609, 3733, 4229, 4903, 11239, 21013, 47507, 65033, 73453, 75629, 105601, 112241, 132499, 172213, 257069, 330641, 361213, 379459, 570029, 667477, 893033, 950633, 976147, 1054717, 1240999, 1435219, 1934837, 2149151, 2775559, 2829011, 3189799
Offset: 1

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Author

Bill McEachen, Feb 14 2021

Keywords

Comments

Conjecture: sequence is infinite.
The generalized Dickson conjecture implies, for example, that there are infinitely many primes p for which p+4, p+6 and p*(p+4)+2*(p+6) = p^2+6*p+12 are prime. - Robert Israel, Mar 22 2021

Examples

			3*5+2*7 = 29 which is prime and so is a(1).
5*7+2*11 = 57 which is composite and so not in the sequence.

Links

Crossrefs

Cf. A000040, A180945.

Programs

  • Maple
    R:= NULL: count:= 0: q:= 2: r:= 3;
while count < 100 do
  p:= q; q:= r; r:=nextprime(r);
  x:= p*q+2*r;
  if isprime(x) then
     count:= count+1; R:= R, x;
  fi
od:
R; # Robert Israel, Mar 22 2021
  • Mathematica
    Select[#1*#2 + 2*#3 & @@@ Partition[Select[Range[2000], PrimeQ], 3, 1], PrimeQ] (* Amiram Eldar, Feb 16 2021 *)
  • PARI
    genit(maxx)={p=List(); forprime(x=3,maxx,q=nextprime(x+1); w=x*q+2*nextprime(q+1); if(isprime(w),listput(p,w)));p;}

A356627 Primes whose powers appear in A332979.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 29, 37, 41, 59, 67, 71, 97, 127, 149, 191, 223, 269, 307, 347, 419, 431, 557, 563, 569, 587, 593, 599, 641, 727, 809, 937, 967, 1009, 1213, 1277, 1423, 1861, 1973, 2237, 2267, 2657, 3163, 3299, 3449, 3457, 3527, 3907, 4001, 4211, 4441, 4637
Offset: 1

Views

Author

Michael De Vlieger, Sep 27 2022

Keywords

Comments

Maxima of row n > 0 of A005940, A182944, and A182945 are powers of these primes.
Indices k of primes, A000040(k), listed here show an interesting correlation with the function f(k) = A000040(k) - A302334(k). - Peter Munn, Sep 29 2022

Examples

			5 | A332979(5..7), thus 5 is in the sequence.
7 | A332979(8), thus 7 is in the sequence.
13 does not divide any term in A332979, so it is not a term in this sequence.

Links

Crossrefs

Cf. A000040, A000961, A005940, A180944, A180945, A302334, A332979.

Programs

  • Mathematica
    Prime@ Union@ Table[MaximalBy[Table[{k, n - k}, {k, n}], Prime[#1]^#2 & @@ # &][[1, 1]], {n, 2^10}]
(* or use concise file in A332979 *)
Prime /@ Union@ Rest@ Map[ToExpression@ StringTrim[#, "p"] & @@ StringSplit[#, "^"] &, Import["https://oeis.org/A332979/a332979.txt", "Data"][[All, -1]]]
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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