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

A136154 Composites one larger than a prime, with exactly five distinct prime factors.

Original entry on oeis.org

2310, 2730, 3990, 4290, 6090, 6270, 7590, 7854, 8610, 8970, 9030, 9240, 9282, 9690, 10010, 10710, 11550, 11970, 12012, 12540, 12810, 13110, 13260, 13398, 13650, 13860, 14322, 14490, 14630, 15330, 15810, 15960, 16302, 16422, 16530, 16830
Offset: 1

Views

Author

Enoch Haga, Dec 16 2007

Keywords

Examples

			a(0)=2310 because 2310 follows the prime 2309 and has five factors 2, 3, 5, 7 and 11.

Crossrefs

Cf. A136151, A136152, A136153, A136155.

Programs

  • PARI
    isok(n) = (omega(n)==5) && isprime(n-1); \\ Michel Marcus, Jun 08 2014

Formula

Equals A008864 INTERSECT A051270. - R. J. Mathar, Feb 20 2008

Extensions

Edited by R. J. Mathar, Feb 20 2008
Typo in a(36) corrected by Seth A. Troisi, May 13 2022
Showing 1-4 of 4 results.

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