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.

A281925 Numbers that are the product of exactly 4 primes and are of the form prime(k) + prime(k + 1).

Original entry on oeis.org

24, 36, 60, 84, 90, 100, 152, 198, 204, 210, 276, 308, 330, 340, 372, 390, 462, 472, 492, 532, 558, 564, 712, 726, 740, 798, 852, 872, 930, 966, 1012, 1148, 1164, 1180, 1192, 1208, 1220, 1230, 1236, 1284, 1290, 1410, 1460
Offset: 1

Views

Author

Zak Seidov, Feb 02 2017

Keywords

Comments

Most but not all terms are multiples of 4.
Intersection of A001043 and A014613. - Bruno Berselli, Feb 02 2017

Examples

			24 = 2^3 * 3 = 11 + 13, 36 = 2^2 * 3^2 = 17 + 19, 60 = 2^2 * 3 * 5 = 29 + 31.

Crossrefs

Cf. A001043, A014613.
Cf. A105936 (products of exactly 3 primes).

Programs

  • Magma
    /* From the second comment: */
a:={n: n in [2..1500] | &+[p[2]: p in Factorization(n)] eq 4};
b:={p+NextPrime(p): p in PrimesUpTo(800)};
a meet b; // Bruno Berselli, Feb 02 2017
  • Mathematica
    Total[#] & /@ Select[Partition[Prime[Range[200]], 2, 1], 4 == PrimeOmega[Total[#]] &]

A281926 Numbers that are the product of exactly 5 primes and are of the form prime(k) + prime(k + 1).

Original entry on oeis.org

112, 120, 162, 300, 396, 450, 456, 520, 630, 684, 696, 702, 752, 828, 882, 918, 924, 990, 1044, 1064, 1140, 1250, 1272, 1300, 1428, 1530, 1650, 1692, 1710, 1716, 1740, 1900, 2032, 2072, 2124, 2156
Offset: 1

Views

Author

Zak Seidov, Feb 02 2017

Keywords

Comments

Note that there is no case of 2 primes.
Intersection of A001043 and A014614. - Bruno Berselli, Feb 02 2017

Examples

			112 = 2^4 * 7 = 53 + 59, 120 = 2^3 * 3 * 5 = 59 + 61, 162 = 2 * 3^4 = 79 + 83.

Links

Crossrefs

Cf. A001043, A014614.
Cf. A105936 (products of 3 primes), A281925 (products of 4 primes).

Programs

  • Mathematica
    Total[#] & /@ Select[Partition[Prime[Range[1000]], 2, 1], 5 == PrimeOmega[Total[#]] &]
  • PARI
    list(lim)=my(v=List()); forprime(p=2,lim\16, forprime(q=2,min(lim\(8*p),p), forprime(r=2,min(lim\(4*p*q),q), forprime(s=2,min(lim\(2*p*q*r),r), my(t=2*p*q*r*s); if(nextprime(t/2)+precprime(t/2)==t, listput(v,t)))))); Set(v) \\ Charles R Greathouse IV, Feb 05 2017

A281927 Numbers that are the product of exactly 10 primes and are of the form prime(n) + prime(n + 1).

Original entry on oeis.org

2304, 3456, 5184, 5376, 8448, 9600, 14400, 14976, 18816, 19008, 19440, 21888, 29440, 30208, 31488, 34048, 36096, 36608, 43264, 43904, 46848, 47040, 47232, 55552, 59520, 60000, 60160, 63936, 69696
Offset: 1

Views

Author

Zak Seidov, Feb 02 2017

Keywords

Comments

Intersection of A001043 and A046314. - Bruno Berselli, Feb 02 2017

Examples

			2304 = 2^8 * 3^2 = 1151 + 1153, 3456 = 2^7 * 3^3 = 1723 + 1733, 5184 = 2^6 * 3^4 = 2591 + 2593.

Crossrefs

Cf. A001043, A046314.
Cf. A105936 (products of 3 primes), A281925 (products of 4 primes), A281926 (products of 5 primes).

Programs

  • Mathematica
    Total[#] & /@ Select[Partition[Prime[Range[10000]], 2, 1], 10 == PrimeOmega[Total[#]] &]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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