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.

A262051 Euler pseudoprimes to base 3: composite integers such that abs(3^((n - 1)/2)) == 1 mod n.

Original entry on oeis.org

121, 703, 1541, 1729, 1891, 2465, 2821, 3281, 4961, 7381, 8401, 8911, 10585, 12403, 15457, 15841, 16531, 18721, 19345, 23521, 24661, 28009, 29341, 30857, 31621, 31697, 41041, 44287, 46657, 47197, 49141, 50881, 52633, 55969, 63139, 63973, 72041, 74593, 75361
Offset: 1

Views

Author

Daniel Lignon, Sep 09 2015

Keywords

Links

Crossrefs

Cf. A006970 (base 2), this sequence (base 3), A001567 (base 4), A262052 (base 5), A262053 (base 6), A262054 (base 7), A262055 (base 8).

Programs

  • Mathematica
    eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[26000] + 1, eulerPseudoQ[#, 3] &] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970 *)
  • PARI
    for(n=1, 1e5, if( Mod(3, (2*n+1))^n == 1 ||  Mod(3, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ Altug Alkan, Oct 11 2015

A262052 Euler pseudoprimes to base 5: composite integers such that abs(5^((n - 1)/2)) == 1 mod n.

Original entry on oeis.org

217, 781, 1541, 1729, 5461, 5611, 6601, 7449, 7813, 11041, 12801, 13021, 13333, 14981, 15751, 15841, 16297, 21361, 23653, 24211, 25351, 29539, 30673, 38081, 40501, 41041, 44173, 44801, 46657, 47641, 48133, 53971, 56033, 67921, 75361, 79381, 90241, 98173, 100651, 102311
Offset: 1

Views

Author

Daniel Lignon, Sep 09 2015

Keywords

Links

Crossrefs

Cf. A006970 (base 2), A262051 (base 3), this sequence (base 5), A262053 (base 6), A262054 (base 7), A262055 (base 8).

Programs

  • Mathematica
    eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[27000] + 1, eulerPseudoQ[#, 5] &] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970 *)
  • PARI
    for(n=1, 1e5, if( Mod(5, (2*n+1))^n == 1 ||  Mod(5, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ Altug Alkan, Oct 11 2015

A262054 Euler pseudoprimes to base 7: composite integers such that abs(7^((n - 1)/2)) == 1 mod n.

Original entry on oeis.org

25, 325, 703, 817, 1825, 2101, 2353, 2465, 3277, 4525, 6697, 8321, 10225, 11041, 11521, 12025, 13665, 14089, 19345, 20197, 20417, 20425, 25829, 29857, 29891, 35425, 38081, 39331, 46657, 49241, 49321, 50881, 58825, 64681, 75241, 75361, 76627, 78937, 79381
Offset: 1

Views

Author

Daniel Lignon, Sep 09 2015

Keywords

Links

Crossrefs

Cf. A006970 (base 2), A262051 (base 3), A262052 (base 5), A262053 (base 6), this sequence (base 7), A262055 (base 8).

Programs

  • Mathematica
    eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[25000] + 1, eulerPseudoQ[#, 7] &] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970 *)
  • PARI
    for(n=1, 1e5, if( Mod(7, (2*n+1))^n == 1 ||  Mod(7, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ Altug Alkan, Oct 11 2015

A262055 Euler pseudoprimes to base 8: composite integers such that abs(8^((n - 1)/2)) == 1 mod n.

Original entry on oeis.org

9, 21, 65, 105, 133, 273, 341, 481, 511, 561, 585, 1001, 1105, 1281, 1417, 1541, 1661, 1729, 1905, 2047, 2465, 2501, 3201, 3277, 3641, 4033, 4097, 4641, 4681, 4921, 5461, 6305, 6533, 6601, 7161, 8321, 8481, 9265, 9709, 10261, 10585, 10745, 11041, 12545
Offset: 1

Views

Author

Daniel Lignon, Sep 09 2015

Keywords

Links

Crossrefs

Cf. A006970 (base 2), A262051 (base 3), A262052 (base 5), A262053 (base 6), A262054 (base 7), this sequence (base 8).

Programs

  • Mathematica
    eulerPseudoQ[n_?PrimeQ, b_] = False; eulerPseudoQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; Select[2 Range[11000] + 1, eulerPseudoQ[#, 8] &] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970 *)
  • PARI
    for(n=1, 1e5, if( Mod(8, (2*n+1))^n == 1 ||  Mod(8, (2*n+1))^n == 2*n && bigomega(2*n+1) != 1 , print1(2*n+1", "))); \\ Altug Alkan, Oct 11 2015

A263239 Euler pseudoprimes to base 9: composite integers such that abs(9^((n - 1)/2)) == 1 mod n.

Original entry on oeis.org

4, 28, 91, 121, 286, 532, 671, 703, 949, 1036, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4636, 4961, 5551, 6364, 6601, 7381, 8401, 8911, 10585, 11011, 11476, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345, 19684, 23521, 24046, 24661, 24727
Offset: 1

Views

Author

Daniel Lignon, Oct 12 2015

Keywords

Comments

Even numbers are permitted since 9 is an integer square. - Charles R Greathouse IV, Oct 12 2015

Links

Crossrefs

Cf. A020138 (pseudoprimes to base 9).
Cf. A006970 (base 2), A262051 (base 3), A262052 (base 5), A262053 (base 6), A262054 (base 7), A262055 (base 8).

Programs

  • Mathematica
    eulerPseudo9Q[n_]:=(Mod[9^((n-1)/2)+1,n]==0 ||Mod[9^((n-1)/2)-1,n]==0) && Not[PrimeQ[n]];
Select[Range[2,200000],eulerPseudo9Q]
  • PARI
    is(n) = abs(centerlift(Mod(3, n)^(n-1)))==1 && !isprime(n) && n>1 \\ Charles R Greathouse IV, Oct 12 2015
Showing 1-5 of 5 results.

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