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 1-5 of 5 results.

A092192 Semiprimes that are the sum of two successive semiprimes.

Original entry on oeis.org

10, 15, 51, 69, 77, 85, 95, 106, 115, 134, 143, 159, 178, 187, 201, 217, 226, 237, 262, 267, 291, 301, 327, 335, 346, 355, 361, 381, 395, 403, 411, 415, 422, 427, 437, 447, 502, 527, 565, 586, 597, 614, 623, 633, 649, 669, 674, 687, 713, 723, 758, 763, 789
Offset: 1

Views

Author

Zak Seidov, Feb 23 2004

Keywords

Examples

			51 is a member because 51=25+26, sum of 9th and 10th semiprimes.

Links

Crossrefs

Cf. A092191.

Programs

  • Mathematica
    Select[Total/@Partition[Select[Range[400],PrimeOmega[#]==2&],2,1], PrimeOmega[ #]==2&] (* Harvey P. Dale, Jan 19 2019 *)

A109311 Numbers n such that sum of n-th and (n+1)-st semiprimes is a square=q^2.

Original entry on oeis.org

6, 17, 58, 78, 89, 122, 187, 219, 229, 278, 313, 353, 367, 552, 589, 966, 1162, 1264, 1530, 1637, 1745, 1928, 2343, 2443, 2540, 2648, 2789, 3649, 3778, 3811, 3900, 4143, 4191, 5038, 5228, 5280, 5426, 5466, 6169, 6613, 6718, 7161, 8225, 9342, 9607
Offset: 1

Views

Author

Zak Seidov, Jun 27 2005

Keywords

Examples

			6 is ok because sp(6)=15, sp(7)=21, 15+21=36=6^2, sp(n)=A001358(n)=n-th semiprime.

Crossrefs

Values of q: A109312. Cf. A001358 = semiprimes, A092191 = numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.

Programs

Formula

sp(n)+sp(n+1)=q^2, sp(n)=n-th semiprime.

Extensions

More terms from Michel Marcus, Oct 06 2013

A109312 Numbers q such that q^2 is a sum of n-th and (n+1)-st semiprimes for some n.

Original entry on oeis.org

6, 10, 19, 22, 24, 28, 35, 38, 39, 43, 46, 49, 50, 62, 64, 83, 92, 96, 106, 110, 114, 120, 133, 136, 139, 142, 146, 168, 171, 172, 174, 180, 181, 199, 203, 204, 207, 208, 222, 230, 232, 240, 258, 276, 280, 288, 289, 294, 300, 304, 310, 321, 325, 326, 327, 328
Offset: 1

Views

Author

Zak Seidov, Jun 27 2005

Keywords

Examples

			6 is ok because sp(6)=15, sp(7)=21, 15+21=36=6^2, sp(n)=A001358(n)=n-th semiprime.

Crossrefs

Values of n: A109311. Cf. A001358 Semiprimes, A092191 Numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.

Programs

  • Maple
    isA001358 := proc(n) option remember ; if numtheory[bigomega](n) = 2 then true; else false ; fi ; end: isA118717 := proc(n) option remember ; local qn,qn1 ; qn := 4 ; while true do qn1 := qn+1 ; while not isA001358(qn1) do qn1 := qn1+1 ; od ; if qn+qn1 =n then RETURN(true) ; elif qn+qn1 > n then RETURN(false) ; fi; qn := qn1 ; od; end: isA109312 := proc(q) isA118717(q^2) ; end: for q from 1 to 500 do if isA109312(q) then printf("%d,",q) ; fi ; od; # R. J. Mathar, Aug 15 2007
  • Mathematica
    Select[Sqrt[#]&/@(Total/@Partition[Select[Range[80000],PrimeOmega[#] == 2&],2,1]),IntegerQ] (* Harvey P. Dale, Dec 11 2018 *)

Formula

q^2=sp(n)+sp(n+1), sp(n)=n-th semiprime.

Extensions

More terms from R. J. Mathar, Aug 15 2007

A109404 Numbers n such that sum of n-th and (n+1)-st semiprimes is a prime.

Original entry on oeis.org

3, 5, 7, 8, 10, 11, 13, 22, 25, 27, 29, 37, 46, 51, 52, 76, 83, 86, 92, 104, 111, 113, 115, 123, 132, 140, 149, 190, 213, 218, 222, 233, 242, 274, 280, 281, 286, 298, 303, 307, 309, 336, 340, 346, 351, 379, 381, 395, 402, 415, 424, 444, 449, 463, 477, 478, 490
Offset: 1

Views

Author

Zak Seidov, Jun 27 2005

Keywords

Examples

			3 is OK because sp(3)=9, sp(3)=10 and 9+10=19 (prime); sp(n)=n-th semiprime.

Crossrefs

Cf. A092191 = numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.

Programs

  • Mathematica
    With[{semis=Partition[Select[Range[2000],PrimeOmega[#]==2&],2,1]}, Flatten[ Position[ semis,?(PrimeQ[Total[#]]&),{1},Heads->False]]] (* _Harvey P. Dale, May 01 2014 *)
  • PARI
    lista(nn) = {vec = vector(nn, i, i); sp = select(i->(bigomega(i)==2), vec); for (i = 1, #sp-1, if (isprime(sp[i]+sp[i+1]), print1(i, ", ")););} \\ Michel Marcus, Oct 06 2013

A109310 Numbers n such that difference between n-th and (n+1)-st semiprimes is a semiprime (sp).

Original entry on oeis.org

4, 6, 18, 21, 23, 30, 36, 42, 43, 50, 68, 76, 78, 80, 87, 88, 91, 98, 108, 111, 116, 117, 118, 120, 127, 128, 134, 138, 141, 150, 151, 152, 153, 156, 164, 168, 171, 179, 185, 186, 192, 195, 196, 204, 212, 215, 216, 226, 232, 236, 237, 244, 245, 250, 255, 266
Offset: 1

Views

Author

Zak Seidov, Jun 27 2005

Keywords

Examples

			4 is ok because sp(4)=10, sp(5)=14, 14-10=sp(1), sp(n)=A001358(n)=n-th semiprime.

Crossrefs

Cf. A001358 = Semiprimes, A092191 = numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.

Programs

  • PARI
    lista(nn) = {vec = vector(nn, i, i); sp = select(i->(bigomega(i)==2), vec); for (i = 1, #sp-1, if (bigomega(sp[i+1]-sp[i]) == 2, print1(i, ", ")););} \\ Michel Marcus, Oct 06 2013
Showing 1-5 of 5 results.

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

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