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.

A233930 Primes p that give record exponents of 2 in p^2 - 1 (A091282).

Original entry on oeis.org

3, 7, 17, 31, 127, 257, 3583, 5119, 6143, 8191, 65537, 131071, 524287, 7340033, 14680063, 104857601, 109051903, 167772161, 469762049, 2013265921, 2147483647, 21474836479, 51539607551, 206158430209, 824633720831, 2748779069441, 6597069766657, 26388279066623
Offset: 1

Views

Author

Michel Marcus, Dec 20 2013

Keywords

Comments

Among these terms, we find the first Mersenne primes (A000668), and some Fermat numbers (A000215).

Examples

			3^2 - 1 = 8 = 2^3. 5 does not beat this record with 5^2 - 1 = 24 = 2^3 * 3.
7^2 - 1 = 48 = 2^4 * 3, so 7 sets the next record, which stands through 11 and 13.
17^2 - 1 = 288 = 2^5 * 3^2.

Links

Programs

  • PARI
    lista(nn) = {r = 0; forprime (n=1, nn, v = valuation(n^2-1, 2); if (v > r, r = v; print1(n, ", ")));}

Extensions

a(22)-a(28) from Hiroaki Yamanouchi, Sep 27 2014

A091283 Exponent of 2 in -1+prime[n]^s, if s is an exponent of the form s=8k-4.

Original entry on oeis.org

0, 4, 4, 5, 4, 4, 6, 4, 5, 4, 7, 4, 5, 4, 6, 4, 4, 4, 4, 5, 5, 6, 4, 5, 7, 4, 5, 4, 4, 6, 9, 4, 5, 4, 4, 5, 4, 4, 5, 4, 4, 4, 8, 8, 4, 5, 4, 7, 4, 4, 5, 6, 6, 4, 10, 5, 4, 6, 4, 5, 4, 4, 4, 5, 5, 4, 4, 6, 4, 4, 7, 5, 6, 4, 4, 9, 4, 4, 6, 5, 4, 4, 6, 6, 5, 4, 8, 5, 4, 6, 4, 7, 5, 4, 4, 5, 4, 5, 4, 4, 4, 4, 4, 5, 4
Offset: 1

Views

Author

Labos Elemer, Jan 22 2004

Keywords

Crossrefs

Cf. A091282, A090739, A090740, A090129, A023506.

Programs

  • Mathematica
    Table[{8*k-4, Table[Part[Flatten[FactorInteger [ -1+Prime[n]^(8*k-4)]], 2], {n, 2, m}]}, {k, 1, 2}]

A091284 Exponent of 2 in -1+prime[n]^s, if s is an exponent of form 16k-8. Except a(1)=0, a(n)=1+A091283(n).

Original entry on oeis.org

0, 5, 5, 6, 5, 5, 7, 5, 6, 5, 8, 5, 6, 5, 7, 5, 5, 5, 5, 6, 6, 7, 5, 6, 8, 5, 6, 5, 5, 7, 10, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 5, 9, 9, 5, 6, 5, 8, 5, 5
Offset: 1

Views

Author

Labos Elemer, Jan 22 2004

Keywords

Comments

Exponents of 2 in -1+p^s if the exponent s[u]=(2^u)k-(2^(u-1) comes from other sequence generated with s[u-1] exponent by adding 1 to terms of the "previous" sequence. E.g. s=256k-128 needed an addition of 6 to the terms of A091282.

Crossrefs

Cf. A023506, A007814, A091282, A091283, A090739, A090740, A090129.

Programs

  • Mathematica
    Table[{8*k-4, Table[Part[Flatten[FactorInteger [ -1+Prime[n]^(16*k-8)]], 2], {n, 2, 50}]}, {k, 1, 2}]
Showing 1-3 of 3 results.

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