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.

A231966 Squarefree numbers (from A005117) with prime divisors in a 2p+1 progression.

Original entry on oeis.org

10, 21, 55, 110, 253, 1081, 1265, 1711, 2530, 3403, 5671, 11891, 13861, 15931, 25651, 34453, 59455, 60031, 64261, 73153, 108811, 114481, 118910, 126253, 158203, 171991, 258121, 351541, 371953, 392941, 482653, 518671, 568301, 703891, 822403, 853471, 869221, 933661
Offset: 1

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Author

Jaroslav Krizek, Nov 16 2013

Keywords

Comments

Squarefree numbers with k>=2 prime divisors of the form p_1 * p_2 * … * p_k, where p_1 < p_2 < … < p_k = primes with p_k = 2 * p_(k-1) + 1.
Supersequence of A156592 (numbers of the form p*q, p and q prime with q=2*p+1; see A005384 and A005385).

Examples

			118910 = 2*5*11*23*47, where 5 = 2*2 + 1, 11 = 2*5 + 1, 23 = 2*11 + 1, 47 = 2*23 + 1.

Crossrefs

Cf. A005117, A156592, A005384, A005385, A000040, A231967, A231968, A231969.

A231967 Squarefree numbers (A005117) of the form p*q*r with prime factors p, q, r with q = 2*p + 1 and r = 2*q + 1.

Original entry on oeis.org

110, 1265, 11891, 568301, 5719229, 46203659, 371436119, 1057570169, 2978731439, 8475105539, 8777935031, 14865764009, 22397944469, 24460553171, 26008879181, 27621202391, 47549400491, 53960155829, 54994829321, 57639193331, 119010782819, 157361958899
Offset: 1

Views

Author

Jaroslav Krizek, Nov 16 2013

Keywords

Comments

Squarefree numbers of the form p*q*r, where p < q < r = primes with q = 2*p + 1 and r = 2*q + 1; that is, r = 4*p + 3.

Examples

			5719229 = 89*179*359, 179 = 2*89 + 1, 359 = 2*179 + 1.

Links

Crossrefs

Cf. A005117, A000040, A231968, A231969, A231966. Cf. A007700 (first member of a prime triple in a 2p+1 progression).

Programs

  • Mathematica
    sfQ[n_]:=Module[{q=2n+1,r},r=2q+1;AllTrue[{q,r},PrimeQ]&& SquareFreeQ[ n*q*r]]; 3#+10#^2+8#^3&/@Select[Prime[Range[400]],sfQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 26 2016 *)

A231969 a(n) = the smallest squarefree number (A005117) with n prime factors in a 2p+1 progression.

Original entry on oeis.org

2, 10, 110, 2530, 118910, 17036047229140531, 4713753689937227789548410467592773787730621935419, 4754361703029497628070972207349674154455369685904736544199583856401, 17434718204270642890620908753958444038404912529730635812020757976125828120134034469
Offset: 1

Views

Author

Jaroslav Krizek, Nov 16 2013

Keywords

Comments

Smallest squarefree numbers with n >= 2 prime divisors of the form p_1 * p_2 * … * p_n, where p_1 < p_2 < … < p_k = primes with p_k = 2 * p_(k-1) + 1.

Examples

			17036047229140531 = 89*179*359*719*1439*2879, where 179 = 2*89 + 1, 359 = 2*179 + 1, 719 = 2*359 + 1, 1439 = 2*719 + 1, 2879 = 2*1439 + 1.

Links

Crossrefs

Cf. A005117, A000040, A231966, A231967, A231968.
Showing 1-3 of 3 results.

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

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