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.

A136151 Composites n with exactly two distinct prime divisors and of the form n=1+(any prime).

Original entry on oeis.org

6, 12, 14, 18, 20, 24, 38, 44, 48, 54, 62, 68, 72, 74, 80, 98, 104, 108, 152, 158, 164, 192, 194, 200, 212, 224, 242, 272, 278, 284, 314, 332, 338, 368, 384, 398, 422, 432, 458, 464, 488, 500, 524, 542, 548, 578, 608, 614, 632, 648, 662, 674, 692, 734, 752, 758
Offset: 1

Views

Author

Enoch Haga, Dec 16 2007

Keywords

Links

Crossrefs

Cf. A136152, A136153, A136154, A136155.

Programs

  • Maple
    isA136151 := proc(n) if isprime(n-1) then if nops(numtheory[factorset](n)) =2 then true; else false ; fi ; else false ; fi ; end: for i from 1 to 200 do n := ithprime(i)+1 ; if isA136151( n) then printf("%d, ",n) ; fi ; od: # R. J. Mathar, Feb 01 2008
  • Mathematica
    Select[Range[800],PrimeNu[#]==2&&PrimeQ[#-1]&] (* Harvey P. Dale, Jun 22 2018 *)

Formula

A008864 INTERSECT A007774. - R. J. Mathar, Feb 01 2008

Extensions

Edited by R. J. Mathar, Feb 01 2008

A136152 Composites one larger than a prime and with exactly three distinct prime factors.

Original entry on oeis.org

30, 42, 60, 84, 90, 102, 110, 114, 132, 138, 140, 150, 168, 174, 180, 182, 198, 228, 230, 234, 240, 252, 258, 264, 270, 282, 294, 308, 312, 318, 348, 350, 354, 360, 374, 380, 402, 410, 434, 440, 444, 450, 468, 480, 492, 504, 522, 558, 564, 572, 588, 594, 600
Offset: 1

Views

Author

Enoch Haga, Dec 16 2007

Keywords

Examples

			a(0)=30 because 30 follows the prime 29 and has three factors 2, 3 and 5.

Links

Crossrefs

Cf. A136151, A136153, A136154, A136155.

Programs

  • Maple
    isA008864 := proc(n) if n -prevprime(n) = 1 then true ; else false ; fi ; end: isA033992 := proc(n) if nops(numtheory[factorset](n)) = 3 then true ; else false ; fi ; end: isA136152 := proc(n) isA008864(n) and isA033992(n) ; end: for n from 1 do p := ithprime(n) ; if isA136152(p+1) then print(p+1) ; fi ; od: # R. J. Mathar, Feb 20 2008
  • Mathematica
    Select[Prime[Range[110]]+1,PrimeNu[#]==3&] (* Harvey P. Dale, Apr 08 2012 *)

Formula

Find primes followed by N with exactly three prime factors, without repetition.
Equals A008864 INTERSECT A033992. - R. J. Mathar, Feb 20 2008

Extensions

Edited by R. J. Mathar, Feb 20 2008

A136153 Composites one larger than a prime, with exactly four distinct prime factors.

Original entry on oeis.org

390, 420, 462, 510, 570, 660, 770, 798, 840, 858, 930, 1020, 1050, 1092, 1110, 1218, 1230, 1260, 1290, 1302, 1320, 1410, 1428, 1430, 1482, 1554, 1560, 1610, 1638, 1710, 1722, 1848, 1890, 1914, 1932, 1950, 1974, 1980, 2030, 2040, 2070, 2090, 2100, 2130
Offset: 1

Views

Author

Enoch Haga, Dec 16 2007

Keywords

Examples

			a(0)=390 because 30 follows the prime 29 and has four prime factors 2, 3, 5 and 13.

Links

Crossrefs

Cf. A136151, A136152, A136154, A136155.

Programs

  • Mathematica
    Select[Prime[Range[400]]+1,PrimeNu[#]==4&] (* Harvey P. Dale, Aug 15 2021 *)
  • PARI
    isok(n) = (omega(n)==4) && isprime(n-1); \\ Michel Marcus, Jun 08 2014

Formula

Equals A008864 INTERSECT A033993. - R. J. Mathar, Feb 20 2008

Extensions

Edited by R. J. Mathar, Feb 20 2008

A136155 Composites one larger than a prime and with exactly two or three distinct prime factors.

Original entry on oeis.org

6, 12, 14, 18, 20, 24, 30, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284, 294
Offset: 1

Views

Author

Enoch Haga, Dec 16 2007

Keywords

Examples

			a(1)=6, which is one larger than the prime 5 and has 2 distinct prime factors (namely 2 and 3).
60 is in the sequence because 59 is prime and 60 = 2^2*3*5 has three distinct prime factors.

Links

Crossrefs

Cf. A136151, A136152, A136153, A136154.

Programs

  • Maple
    A001221 := proc(n) nops(numtheory[factorset](n)) ; end: isA136155 := proc(n) if isprime(n-1) then RETURN( A001221(n)=2 or A001221(n)= 3) ; else RETURN(false) ; fi ; end: for n from 1 to 300 do if isA136155(n) then printf("%d,",n) ; fi ; od: # R. J. Mathar, May 03 2008
  • Mathematica
    okQ[n_] := PrimeQ[n-1] && (PrimeNu[n]==2 || PrimeNu[n]==3);
Select[Range[6, 300, 2], okQ] (* Jean-François Alcover, Feb 04 2023 *)

Formula

Union of A136151 and A136152. Subset of A008864. - R. J. Mathar, Apr 24 2008
A136151 UNION A136152. - R. J. Mathar, May 03 2008

Extensions

Edited by R. J. Mathar and Jens Kruse Andersen, Apr 24 2008
Showing 1-4 of 4 results.

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