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 1-4 of 4 results.

A165768 Smallest prime factor of the semiprime 2^A165767(n)-A165767(n).

Original entry on oeis.org

2, 11, 7, 2, 271, 6733, 41, 11, 2, 3769453, 77647, 2, 541, 1394161003757, 13806493, 5, 3, 1778463179021, 193, 19, 17377902756647509, 398407, 3, 389, 137, 137867, 3, 3, 160038737, 739, 4889866261929241, 37, 5, 48109, 3190436507
Offset: 1

Views

Author

M. F. Hasler, Oct 08 2009

Keywords

Comments

a(n)=2 whenever A165767(n) is even.

Examples

			17377902756647509 is in this sequence because it is the smallest prime factor of the semiprime 2^199-199.

Links

Formula

a(n) = (2^A165767(n)-A165767(n))/A165769(n).

Extensions

More terms from Max Alekseyev, Dec 13 2011

A165769 Largest prime factor of the semiprime 2^A165767(n)-A165767(n).

Original entry on oeis.org

29, 11, 4679, 131063, 123817, 318949, 209510599, 49977801259, 2199023255531, 9334079, 7250118529, 2305843009213693921, 17457916757373919459, 27748320404471, 717308900550128276543, 2028240960365167042394725128581, 221537999297485978817301176713390723
Offset: 1

Views

Author

M. F. Hasler, Oct 08 2009

Keywords

Comments

A165768(n)=2 <=> A165767(n)=2k for some k <=> a(n)=4^k/2-k is prime. This is the case for k=3,9,21,31,1125,...

Examples

			46235097144973199564251065756966919577339221 is in this sequence because it is the largest prime factor of the semiprime 2^199-199.

Links

Formula

a(n)=(2^A165767(n)-A165767(n))/A165768(n).

A252656 Numbers n such that 3^n - n is a semiprime.

Original entry on oeis.org

4, 6, 10, 25, 28, 32, 98, 124, 146, 164, 182, 190, 200, 220, 226, 230, 248, 280, 362, 376, 418, 446, 518, 544
Offset: 1

Views

Author

Vincenzo Librandi, Dec 20 2014

Keywords

Comments

Are there odd members of the sequence other than 25? There are no others < 10000. An odd number m is in the sequence iff (3^m - m)/2 is prime. - Robert Israel, Jan 02 2015
No more odd terms after a(4) = 25 for m < 200000. a(25) >= 626. - Hugo Pfoertner, Aug 07 2019

Examples

			4 is in this sequence because 3^4 - 4 = 7*11 is semiprime.
10 is in this sequence because 3^10 - 10 = 43*1373 and these two factors are prime.

Links

Crossrefs

Cf. numbers m such that k^m - m is a semiprime: A165767 (k = 2), this sequence (k = 3), A252657 (k = 4), A252658 (k = 5), A252659 (k = 6), A252660 (k = 7), A252661 (k = 8), A252662 (k = 9), A252663 (k = 10).
Cf. A001358 (semiprimes), A058037, A252788.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [2..150] | IsSemiprime(s) where s is 3^m-m];
  • Maple
    select(n -> numtheory:-bigomega(3^n - n) = 2, [$1..150]); # Robert Israel, Jan 02 2015
  • Mathematica
    Select[Range[150], PrimeOmega[3^# - #] == 2 &]
  • PARI
    is(m) = bigomega(3^m-m)==2 \\ Felix Fröhlich, Dec 30 2014
  • PARI
    n=1;while(n<100,s=3^n-n;c=0;forprime(p=1,10^4,if(s%p,c++);if(s%p==0,s1=s/p;if(ispseudoprime(s1),print1(n,", ");c=0;break);if(!ispseudoprime(s1),c=0;break)));if(!c,n++);if(c,if(bigomega(s)==2,print1(n,", "));n++)) \\ Derek Orr, Jan 02 2015

Extensions

a(10) from Felix Fröhlich, Dec 30 2014
a(11)-a(14) from Charles R Greathouse IV, Jan 02 2015
a(15)-a(24) from Luke March, Aug 21 2015

A085745 Numbers m such that 2^m + m is a semiprime.

Original entry on oeis.org

2, 11, 23, 34, 59, 69, 87, 95, 119, 123, 129, 171, 197, 239, 341, 425, 455, 471, 515, 519, 635, 765, 959, 1115, 1181, 1210
Offset: 1

Views

Author

Jason Earls, Jul 21 2003

Keywords

Comments

a(27) >= 1239. If 1239 is not a term then a(27) = 1275. - Amiram Eldar, Oct 26 2024

Links

Crossrefs

Cf. A006127, A052007, A089535, A089536, A089537.
Sequences A165767, A165768, A165769 are the analog for 2^n-n. - M. F. Hasler, Oct 08 2009

Programs

  • Mathematica
    Select[Range[1300],PrimeOmega[2^#+#]==2&] (* Harvey P. Dale, Dec 18 2014 *)

Formula

a(n) = 2*k <=> A089535(n) is even <=> A089536(n) = 2 <=> A089537(n) = 4^k/2 + k, and for any prime of this form, there is a term a(n) = 2*k in this sequence. - M. F. Hasler, Oct 08 2009

Extensions

More terms from Ray Chandler, Nov 08 2003
a(15) from Donovan Johnson, Mar 06 2008
a(16)-a(26) from Sean A. Irvine, Oct 27 2009
Offset changed to 1 by Jinyuan Wang, Jul 30 2021
Showing 1-4 of 4 results.

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