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 1-6 of 6 results.

A161689 Intersection of A151740 and A151741.

Original entry on oeis.org

49, 99, 153, 161, 171, 175, 185, 189, 221, 231, 235, 243, 247, 265, 285, 289, 319, 329, 341, 351, 369, 375, 391, 405, 429, 435, 441, 469, 473, 495, 507, 517, 531, 535, 545, 549, 581, 589, 603, 609, 639, 645, 651, 657, 667, 671, 679, 689, 711, 715, 725, 729
Offset: 1

Views

Author

Zak Seidov, Jun 17 2009

Keywords

Comments

Composite numbers that are sum of two and three consecutive composite numbers. Provably only odd integers.

Examples

			49=24+25=15+16+18
99=49+50=32+33+34
153=76+77=50+51+52.

Links

Crossrefs

A151740, A151741, A151745.

Programs

  • Mathematica
    Module[{c=Select[Range[800],CompositeQ],s2,s3},s2=Total/@Partition[c,2,1];s3=Total/@Partition[c,3,1];Intersection[c,s2,s3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 27 2019 *)

A151741 Composite which are the sum of three consecutive composite numbers.

Original entry on oeis.org

18, 27, 36, 45, 49, 54, 63, 75, 78, 81, 85, 90, 95, 99, 102, 105, 117, 121, 126, 135, 143, 147, 150, 153, 161, 165, 168, 171, 175, 180, 185, 189, 192, 195, 203, 207, 216, 221, 225, 228, 231, 235, 243, 247, 255, 258, 261, 265, 273, 276, 279, 282, 285, 289, 297
Offset: 1

Views

Author

Claudio Meller, Jun 15 2009

Keywords

Crossrefs

Cf. A151740-A151745, A060254, A060327, A060339, A096785, A096787, A135170.

Programs

  • Mathematica
    Module[{c=Select[Range[300],CompositeQ],s3},s3=Total/@Partition[c,3,1];Intersection[c,s3]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 27 2019 *)
  • PARI
    c1=4;c2=6;for(c3=8,299,isprime(c3) && next;isprime(c1+c2+c3) || print1(c1+c2+c3",");c1=c2;c2=c3) \\ M. F. Hasler, Jun 16 2009

A151742 Composite numbers which are the sum of four consecutive composite numbers.

Original entry on oeis.org

27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 92, 102, 106, 111, 117, 123, 129, 134, 138, 143, 148, 153, 159, 165, 171, 177, 183, 188, 198, 202, 207, 212, 217, 222, 226, 231, 237, 243, 249, 254, 258, 268, 273, 279, 285, 291, 297, 302
Offset: 1

Views

Author

Claudio Meller, Jun 15 2009

Keywords

Links

Crossrefs

Cf. A151740, A151741, A151743.

Programs

  • Mathematica
    Select[Total/@Partition[Select[Range[100],CompositeQ],4,1],CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 21 2020 *)

Extensions

Definition clarified by Harvey P. Dale, Apr 21 2020

A151745 Composites that are the sum of two, three, four and five consecutive composite numbers.

Original entry on oeis.org

405, 1395, 3435, 3525, 4245, 4365, 6675, 6885, 7155, 7515, 7995, 8325, 8445, 9075, 10365, 10845, 11205, 11543, 13005, 14235, 14325, 18075, 19725, 19875, 22605, 23257, 23475, 23617, 26805, 27315, 29835, 29955, 31035, 32355, 32925, 33165, 34395
Offset: 1

Views

Author

Claudio Meller, Jun 15 2009

Keywords

Examples

			405 is in the list because it is composite and
405 = 202 + 203 (Sum of two consecutive composite numbers)
405 = 134 + 135 + 136 (Sum of three consecutive composite numbers)
405 = 99 + 100 + 102 + 104 (Sum of four consecutive composite numbers)
405 = 78 + 80 + 81 + 82 + 84 (Sum of five consecutive composite numbers).

Links

Programs

  • Maple
    N:= 10^5: # for terms <= N
Comps:= remove(isprime, [$2..N]):
PSComps:= [0,op(ListTools:-PartialSums(Comps))]:
C2:= convert(PSComps[3..-1]-PSComps[1..-3],set):
C3:= convert(PSComps[4..-1]-PSComps[1..-4],set):
C4:= convert(PSComps[5..-1]-PSComps[1..-5],set):
C5:= convert(PSComps[6..-1]-PSComps[1..-6],set):
R:= convert(Comps,set) intersect C2 intersect C3 intersect C4 intersect C5:
sort(convert(R,list)); # Robert Israel, Aug 17 2020
  • Mathematica
    CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; q=8!; lst2={};Do[If[ !PrimeQ[n],c=CompositeNext[n];a2=n+c;If[ !PrimeQ[a2],AppendTo[lst2,a2]]],{n,q}];lst2; lst3={};Do[If[ !PrimeQ[n],c1=CompositeNext[n];c2=CompositeNext[c1];a3=n+c1+c2;If[ !PrimeQ[a3],AppendTo[lst3,a3]]],{n,q}];lst3; lst4={};Do[If[ !PrimeQ[n],c1=CompositeNext[n];c2=CompositeNext[c1];c3=CompositeNext[c2];a4=n+c1+c2+c3;If[ !PrimeQ[a4],AppendTo[lst4,a4]]],{n,q}];lst4; lst5={};Do[If[ !PrimeQ[n],c1=CompositeNext[n];c2=CompositeNext[c1];c3=CompositeNext[c2];c4=CompositeNext[c3];a5=n+c1+c2+c3+c4;If[ !PrimeQ[a5],AppendTo[lst5,a5]]],{n,q}];lst5; Intersection[lst2,lst3,lst4,lst5] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2009 *)

Formula

Intersection of A151740, A151741, A151742 and A151743. - R. J. Mathar, Jun 17 2009

Extensions

Corrected and extended by Harvey P. Dale, Nov 25 2014
Corrected by Robert Israel, Aug 17 2020

A151743 Composite which are the sum of five consecutive composite numbers.

Original entry on oeis.org

45, 60, 75, 90, 105, 112, 118, 124, 130, 136, 143, 150, 164, 170, 176, 182, 188, 195, 203, 210, 217, 225, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 300, 314, 320, 326, 332, 338, 345, 360, 374, 380, 386, 392, 398, 405
Offset: 1

Views

Author

Claudio Meller, Jun 15 2009

Keywords

Crossrefs

Cf. A151740, A151741, A151742.

A167611 Nonprimes that are the sum of two consecutive nonprimes.

Original entry on oeis.org

1, 10, 14, 22, 26, 34, 38, 46, 49, 51, 55, 58, 62, 65, 69, 74, 77, 82, 86, 91, 94, 99, 106, 111, 115, 118, 122, 125, 129, 134, 142, 146, 153, 155, 158, 161, 166, 169, 171, 175, 178, 183, 185, 187, 189, 194, 202, 206, 209, 214, 218, 221, 226, 231, 235, 237, 243
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 07 2009

Keywords

Comments

One and composite numbers that are the sum of two consecutive composite numbers.
Essentially the same as A151740 (except for initial term 1). - Georg Fischer, Oct 01 2018

Examples

			a(1) = 1st nonprime + 2nd nonprime = 0 + 1 =  1, which is nonprime;
a(2) = 3rd nonprime + 4th nonprime = 4 + 6 = 10, which is nonprime.

Links

Crossrefs

Cf. A018252, A141468, A151740.

Programs

  • Magma
    m:=150; NonPrime:=[i: i in [0..m] | not IsPrime(i)]; [q: n in [1..#NonPrime-1] | not IsPrime(q) where q is NonPrime[n]+NonPrime[n+1]]; // Bruno Berselli, Apr 05 2014
  • Python
    from sympy import isprime, composite
print([1] + [totest for k in range(1,91) if not isprime(totest := composite(k) + composite(k+1))]) # Karl-Heinz Hofmann, Jan 25 2024

Extensions

Entries confirmed by R. J. Mathar, May 30 2010
Showing 1-6 of 6 results.

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