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 1-6 of 6 results.

A152023 Numbers in A152022 which are not products of terms of A152021.

Original entry on oeis.org

65, 260, 273, 325, 1025, 1029, 1040, 1045, 1092, 1105, 1281, 1300, 1345, 1365, 4097, 4100, 4116, 4160, 4165, 4180, 4368, 4420, 4433, 5124, 5125, 5185, 5200, 5380, 5460, 16385, 16388, 16400, 16401, 16405, 16464, 16465, 16640, 16645, 16660, 16705, 16709, 16720
Offset: 1

Views

Author

Vladimir Shevelev, Nov 20 2008, Jun 11 2009

Keywords

Crossrefs

Cf. A000695, A152021, A152022.

Programs

  • Mathematica
    f[n_] := FromDigits[IntegerDigits[n, 2], 4];  s = Array[f, 300, 2]; div[a_, b_] := Divisible[a, b] && a > b; n = 1; s0 = s; While[Length[s] > n, s = Select[s, ! div[#, s[[n]]] &]; n++]; s1 = Complement[s0, s]; aQ[n_, s_] := Times @@ (s^(IntegerExponent[n, #] & /@ s)) == n; Select[s1, ! aQ[#, s] &] (* Amiram Eldar, Aug 31 2019 *)

Extensions

a(12)-a(14) inserted and more terms added by Amiram Eldar, Aug 31 2019

A152079 Primes p such that A000695(p) are also prime.

Original entry on oeis.org

3, 5, 17, 23, 29, 43, 47, 53, 61, 83, 107, 139, 149, 151, 173, 179, 181, 191, 229, 233, 239, 257, 263, 269, 277, 307, 353, 379, 383, 389, 409, 439, 443, 449, 479, 503, 563, 569, 631, 647, 653, 661, 673, 743, 787, 823, 863, 877, 929, 967, 983
Offset: 1

Views

Author

Vladimir Shevelev, Nov 23 2008

Keywords

Comments

Numbers a(n) are in A077718. Conjecture: The sequence contains infinitely many terms.
Supporting the conjecture, there are 8398 terms up to a million, 56915 up to 10 million, 407875 terms up to 100 million, and 3135962 terms up to a billion. - Charles R Greathouse IV, Apr 28 2015

Links

Crossrefs

Cf. A000695, A077718, A152021, A152022, A152023, A152078.

Programs

Extensions

More terms derived from b000695.txt by Michel Marcus, Jun 02 2013

A152078 Numbers a(n) for which A000695(a(n)) = A077718(n).

Original entry on oeis.org

3, 5, 17, 23, 29, 43, 47, 53, 55, 61, 77, 83, 87, 91, 107, 115, 117, 121, 139, 149, 151, 171, 173, 179, 181, 185, 191, 203, 213, 229, 233, 239, 253, 257, 263, 269, 277, 299, 307, 327, 329, 353, 369, 379, 383, 389, 405, 409, 415, 425, 439, 443, 449, 471, 475, 477
Offset: 1

Views

Author

Vladimir Shevelev, Nov 23 2008

Keywords

Examples

			If n=1, then a(1)=3, A000695(3)=5=A077718(1).

Crossrefs

Cf. A000695, A077718, A152021, A152022, A152023.

Programs

  • Mathematica
    f[n_] := FromDigits[IntegerDigits[n, 2], 4]; Select[Range[500], PrimeQ[f[#]] &] (* Amiram Eldar, Aug 31 2019 *)

Extensions

More terms from Amiram Eldar, Aug 31 2019

A152080 Composite numbers c for which A000695(c) is prime.

Original entry on oeis.org

55, 77, 87, 91, 115, 117, 121, 171, 185, 203, 213, 253, 299, 327, 329, 369, 405, 415, 425, 471, 475, 477, 481, 493, 501, 539, 583, 625, 637, 665, 675, 687, 721, 755, 789, 803, 805, 815, 817, 833, 835, 841, 855, 861, 913, 935, 955, 973, 979, 981
Offset: 1

Views

Author

Vladimir Shevelev, Nov 23 2008

Keywords

Crossrefs

Cf. A000695, A077718, A152021, A152022, A152023, A152078, A152079.

Programs

  • Mathematica
    f[n_] := FromDigits[IntegerDigits[n, 2], 4]; Select[Range[1000], CompositeQ[#] && PrimeQ[f[#]] &] (* Amiram Eldar, Dec 13 2018 *)
  • PARI
    a000695(n) = fromdigits(binary(n), 4);
lista(nn) = forcomposite(n=1, nn, if (isprime(a000695(n)), print1(n, ", "))); \\ Michel Marcus, Dec 13 2018

Extensions

More terms derived from b000695.txt by Michel Marcus, Jun 02 2013

A152081 Least prime divisor of terms of A152080.

Original entry on oeis.org

5, 7, 3, 7, 5, 3, 11, 3, 5, 7, 3, 11, 13, 3, 7, 3, 3, 5, 5, 3, 5, 3, 13, 17, 3, 7, 11, 5, 7, 5, 3, 3, 7, 5, 3, 11, 5, 5, 19, 7, 5, 29, 3, 3, 11, 5, 5, 7, 11, 3, 7, 29, 5, 3, 3, 19, 3, 3, 3, 13, 5, 7, 29, 7, 31, 3, 23, 17, 13, 13, 3, 19, 3, 3, 7, 3, 5, 7, 3, 11, 11, 29, 37
Offset: 1

Views

Author

Vladimir Shevelev, Nov 23 2008

Keywords

Crossrefs

Cf. A020639, A152080, A000625, A152021, A152022, A152023, A152078.

Programs

  • PARI
    a000695(n) = fromdigits(binary(n), 4);
lista(nn) = forcomposite(n=1, nn, if (isprime(a000695(n)), print1(factor(n)[1,1], ", "))); \\ Michel Marcus, Dec 18 2018

Formula

a(n) = A020639(A152080(n)). - Michel Marcus, Sep 24 2023

Extensions

More terms from Michel Marcus, Jun 02 2013
More terms from Michel Marcus, Dec 18 2018

A152082 Largest prime divisors of the terms of A152080.

Original entry on oeis.org

11, 11, 29, 13, 23, 13, 11, 19, 37, 29, 71, 23, 23, 109, 47, 41, 5, 83, 17, 157, 19, 53, 37, 29, 167, 11, 53, 5, 13, 19, 5, 229, 103, 151, 263, 73, 23, 163, 43, 17, 167, 29, 19, 41, 83, 17, 191, 139, 89, 109, 149, 37, 43, 73, 53, 59, 5, 379, 383, 89, 233, 167
Offset: 1

Views

Author

Vladimir Shevelev, Nov 23 2008

Keywords

Crossrefs

Cf. A000695, A152021, A152022, A152023, A152078, A152080.

Programs

  • Mathematica
    f[n_] := FromDigits[IntegerDigits[n, 2], 4]; pmax[n_] := FactorInteger[n][[-1, 1]]; pmax /@ Select[Range[1300], CompositeQ[#] && PrimeQ[f[#]] &] (* Amiram Eldar, Aug 31 2019 *)

Extensions

More terms from Amiram Eldar, Aug 31 2019
Showing 1-6 of 6 results.

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