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.

A245427 Primes of the form n^6 - n^5 + n^4 - n^3 + n^2 - n + 1.

Original entry on oeis.org

43, 547, 909091, 1623931, 7027567, 10678711, 15790321, 22796593, 32222107, 81867661, 183458857, 234750601, 574995877, 2498207293, 6177695707, 7095062437, 9272716111, 13564461457, 19397579293, 24344094727, 50689400581, 81420308971, 137405657593, 149289169177
Offset: 1

Views

Author

K. D. Bajpai, Jul 21 2014

Keywords

Comments

All the terms in this sequence are primes, but none are congruent to 9 mod 10.
All terms == 1 (mod 7). - Robert Israel, Jul 22 2014

Examples

			n = 2: n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 = 43, which is prime.
n = 10: n^6 - n^5 + n^4 - n^3 + n^2 - n + 1 = 909091, which is prime.
		

Crossrefs

Programs

  • Mathematica
    Select[Table[n^6 - n^5 + n^4 - n^3 + n^2 - n + 1, {n, 200}], PrimeQ]

A245482 Semiprimes of the form m^6 - m^5 + m^4 - m^3 + m^2 - m + 1.

Original entry on oeis.org

3277, 13021, 102943, 233017, 478297, 2756293, 44693587, 465273397, 705483871, 859769191, 2117950381, 3996097561, 8123248981, 10554648343, 11980986577, 15318627451, 21753909997, 30299909641, 33705129193, 37423460467, 41477524747, 45891147541, 97434620557, 106376475037
Offset: 1

Views

Author

K. D. Bajpai, Jul 23 2014

Keywords

Comments

All the terms in this sequence are odd semiprimes.
Primes of this form are at A245427.

Examples

			m = 4: m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 3277 = 29 * 113, which is semiprime and appears in the sequence.
m = 5: m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 13021 = 29 * 449, which is semiprime and appears in the sequence.
		

Crossrefs

Programs

  • Mathematica
    A245482 = {}; k = n^6 - n^5 + n^4 - n^3 + n^2 - n + 1; Do[If[PrimeOmega[k] == 2, AppendTo[A245482, k]], {n, 100}]; A245482
  • PARI
    for(n=1,100,s=sum(i=0,6,(-n)^i);if(bigomega(s)==2,print1(s,", "))) \\ Derek Orr, Jul 28 2014

A245483 Semiprimes of the form m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1.

Original entry on oeis.org

44287, 838861, 247165843, 3138105961, 269971011311, 540609741211, 1034834473201, 3382547898907, 5824512944911, 9752380952381, 25405143539623, 91699453500601, 406683658856861, 794014903012651, 2005395532515211, 7936895933061811, 10230009756097561, 13103072183720201
Offset: 1

Views

Author

K. D. Bajpai, Jul 23 2014

Keywords

Comments

All the terms in sequence are odd semiprimes, but none is congruent to 5 or 9 (mod 10).

Examples

			m = 3: m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 44287 = 67 * 661, which is semiprime and appears in the sequence.
m = 7: m^10 - m^9 + m^8 - m^7 + m^6 - m^5 + m^4 - m^3 + m^2 - m + 1 = 247165843 = 23 * 10746341, which is semiprime and appears in the sequence.
		

Crossrefs

Programs

  • Mathematica
    A245483 = {}; k = n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1; Do[If[PrimeOmega[k] == 2, AppendTo[A245483, k]], {n, 100}]; A245483
    Select[Table[1-n+n^2-n^3+n^4-n^5+n^6-n^7+n^8-n^9+n^10,{n,100}],PrimeOmega[ #] ==2&] (* Harvey P. Dale, Oct 10 2018 *)
  • PARI
    for(n=1,10^3,s=sum(i=0,10,(-n)^i);if(bigomega(s)==2,print1(s,", "))) \\ Derek Orr, Aug 03 2014
Showing 1-3 of 3 results.