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.

A137625 The initial prime in the first set of n consecutive primes for which p+4 is semiprime.

Original entry on oeis.org

2, 29, 173, 709, 1741, 8297, 8297, 19213, 175229, 175229, 33952609, 4377722623, 4377722623, 1242030992173, 1242030992173
Offset: 1

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Author

Enoch Haga, Jan 30 2008

Keywords

Comments

Suggested by Carlos Rivera's Puzzle 429 which asks for runs where p+2 is biprime.

Examples

			a(2)=29 because this is the first prime in a run of 2 consecutive primes -- 29 and 31 -- where p+4 is semiprime, i.e., 29+4 and 31+4 are both semiprimes.
		

Crossrefs

Programs

  • UBASIC
    10 'p+4 is biprime 20 N=1 30 A=3:S=sqrt(N) 40 B=N\A: if B*A=N then N=N+2:goto 30 50 A=A+2: if A<=S then 40 60 C=C+1:O=N+4:D=prmdiv(O):E=O\D 70 if E<>prmdiv(E) or E=1 then C=0:goto 90 80 print C;N;D;E;O: if C>=10 then stop 90 N=N+2:goto 30

Extensions

a(1) corrected and a(11)-a(15) from Giovanni Resta, Jun 22 2018
Example clarified by Harvey P. Dale, Jan 18 2025

A137626 The largest prime in the first set of n consecutive primes for which p+4 is semiprime.

Original entry on oeis.org

2, 31, 181, 733, 1777, 8363, 8369, 19273, 175333, 175349, 33952819, 4377722977, 4377723013, 1242030992717, 1242030992723
Offset: 1

Views

Author

Enoch Haga, Jan 30 2008

Keywords

Comments

a(n) = last prime in the first run of n primes such that p+4 is semiprime for each prime p in the run. - Sean A. Irvine, Feb 13 2012
a(n) > 5 * 10^9 for n > 13.

Examples

			a(2)=31 is the largest in a set of 2 consecutive primes {29,31}, and 29 + 4 = 33 = 3*11 and 31 + 4 = 35 = 5*7 are both semiprime.  No smaller number has this property.
59 is not in the sequence because although 47 + 4 = 51 = 3*17 and 53 + 4 = 57 = 3*19 are both semiprime, 59 + 4 = 63 = 3*3*7 is not.
		

Crossrefs

Subsequence of A289250.

Programs

  • Mathematica
    With[{prs=Table[If[PrimeOmega[n+4]==2,1,0],{n,Prime[Range[21*10^5]]}]}, Prime[ #]&/@Flatten[Table[SequencePosition[prs,PadRight[{},n,1],1],{n,11}],1]][[All,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2018 *)
  • PARI
    a(n) = {my(t = 0); forprime(p = 2, oo, if(bigomega(p + 4) == 2, t++; if(t==n, return(p)), t = 0))} \\ David A. Corneth, May 10 2018

Extensions

a(11) from Sean A. Irvine, Feb 12 2012
a(1) corrected by Harvey P. Dale, May 10 2018
a(12)-a(13) from David A. Corneth, May 10 2018
a(14)-a(15) from Giovanni Resta, Jun 22 2018

A137627 Semiprimes (p+4) associated with first prime in A137625.

Original entry on oeis.org

6, 33, 177, 713, 1745, 8301, 8301, 19217, 175233, 175233, 33952613, 4377722627, 4377722627, 1242030992177, 1242030992177
Offset: 1

Views

Author

Enoch Haga, Jan 30 2008

Keywords

Comments

Some terms may overlap: e.g., k=9 and k=10 both begin with p=175229 where p+4 = 175233.

Examples

			a(2)=33 because if p=29, then p+4 is 33 and semiprime (3*11).
		

Crossrefs

Formula

For each p, the semiprime is p+4.

Extensions

a(1) corrected by and a(11)-a(15) from Giovanni Resta, Jun 22 2018
Showing 1-3 of 3 results.