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 1-3 of 3 results.

A369056 Numbers k of the form 4m+3 for which there is no representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

Original entry on oeis.org

3, 7, 11, 15, 19, 23, 31, 35, 43, 47, 59, 63, 67, 79, 83, 99, 107, 115, 127, 139, 143, 159, 163, 171, 175, 179, 207, 219, 223, 227, 235, 243, 259, 279, 283, 295, 303, 307, 319, 323, 339, 347, 367, 379, 387, 399, 403, 415, 427, 443, 463, 499, 515, 523, 531, 547, 559, 571, 579, 595, 603, 619, 639, 643, 655, 659, 675
Offset: 1

Views

Author

Antti Karttunen, Jan 20 2024

Keywords

Comments

Numbers k in A004767 for which A369054(k) = 0.
Numbers k of the form 4m-1 such that they are not arithmetic derivative (A003415) of any term of A046316.
Question: Is it possible that this sequence might be finite (although very long)? See comments in A369055.

Links

Crossrefs

Setwise difference A004767 \ A369251.
Cf. A003415, A046316, A369054, A369055.
Subsequences: A369248 (terms that are multiples of 3), A369249 (primes in this sequence).
Cf. also A369250 (4m+3 primes missing from this sequence).

Programs

  • Maple
    N:= 1000: # for terms <= N
S:= {seq(i,i=3..N,4)}:
P:= select(isprime, [seq(i,i=3..N/3,2)]):
for i from 1 to nops(P) do
  p:= P[i];
  for j from i to nops(P) do
    q:= P[j];
    if 2*p*q + q^2 > N then break fi;
    for k from j to nops(P) do
      r:= P[k];
      v:= p*q + p*r + q*r;
      if v > N then break fi;
      S:= S minus {v};
od od od:
sort(convert(S,list)); # Robert Israel, Apr 17 2024
  • PARI
    isA369056(n) = ((3==(n%4)) && !A369054(n)); \\ Needs also program from A369054.

A369251 Numbers that have at least one representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

Original entry on oeis.org

27, 39, 51, 55, 71, 75, 87, 91, 95, 103, 111, 119, 123, 131, 135, 147, 151, 155, 167, 183, 187, 191, 195, 199, 203, 211, 215, 231, 239, 247, 251, 255, 263, 267, 271, 275, 287, 291, 299, 311, 315, 327, 331, 335, 343, 351, 355, 359, 363, 371, 375, 383, 391, 395, 407, 411, 419, 423, 431, 435, 439, 447, 451, 455, 459
Offset: 1

Views

Author

Antti Karttunen, Jan 22 2024

Keywords

Comments

By necessity all terms are of the form 4m+3 (in A004767).

Links

Crossrefs

Complement of A369464.
Sequence A369252 sorted into ascending order, with duplicates removed.
Setwise difference A004767 \ A369056.
Subsequence of A239433.
Cf. A369054, A369055.
Cf. A369250 (primes in this sequence).

Programs

  • PARI
    isA369251(n) = if(3!=(n%4),0, my(v = [3,3], ip = #v, r); while(1, r = (n-(v[1]*v[2])) / (v[1]+v[2]); if(r < v[2], ip--, ip = #v; if(1==denominator(r) && isprime(r), return(1))); if(!ip, return(0)); v[ip] = nextprime(1+v[ip]); for(i=1+ip,#v,v[i]=v[i-1])));

Formula

{k | A369054(k) > 0}.

A369249 Primes of the form 4*m+3 for which there is no representation as a sum (p*q + p*r + q*r) with three odd primes p <= q <= r.

Original entry on oeis.org

3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 79, 83, 107, 127, 139, 163, 179, 223, 227, 283, 307, 347, 367, 379, 443, 463, 499, 523, 547, 571, 619, 643, 659, 683, 787, 827, 883, 907, 947, 967, 1039, 1087, 1123, 1171, 1259, 1327, 1423, 1459, 1483, 1523, 1567, 1579, 1627, 1699, 1723, 1747, 1759, 1787, 1987, 1999, 2083, 2143
Offset: 1

Views

Author

Antti Karttunen, Jan 22 2024

Keywords

Links

Crossrefs

Intersection of A002145 and A369056.
Setwise difference A002145 \ A369250.
Cf. A369054.
Cf. also A189483.

Programs

Showing 1-3 of 3 results.

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

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