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.

A163602 First differences of A161753.

Original entry on oeis.org

1, 15, 20, 28, 17, 19, 44, 52, 29, 31, 68, 76, 41, 43, 92, 49, 51, 53, 55, 116, 124, 65, 67, 69, 71, 148, 77, 79, 164, 172, 89, 91, 188, 97, 99, 101, 103, 212, 109, 111, 113, 115, 236, 244, 125, 127, 129, 131, 268, 137, 139, 284, 292, 149, 151, 153, 155, 316, 161, 163, 332
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 01 2009

Keywords

Examples

			a(1)=1=1^2-0^2. a(2)=15=4^2-1^2. a(3)=20=6^2-4^2.
		

Crossrefs

Programs

  • Maple
    A141468 := proc(n) if n <= 2 then n-1 ; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end;
    A161753 := proc(n) A141468(n)^2 ; end:
    A163602 := proc(n) A161753(n+1)-A161753(n) ; end: seq(A163602(n),n=1..100) ; # R. J. Mathar, Aug 07 2009
  • Mathematica
    A161753 := With[{nn = 500}, Complement[Range[0, nn], Prime[Range[PrimePi[nn]]]]^2]; Table[A161753[[n + 1]] - A161753[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 29 2017 *)
    Differences[With[{nn=100},Complement[Range[0,nn],Prime[Range[ PrimePi[ nn]]]]^2]] (* Harvey P. Dale, Mar 03 2020 *)

Formula

a(n) = A161753(n+1) - A161753(n).

Extensions

a(6) corrected by R. J. Mathar, Aug 07 2009

A161757 a(n) = (prime(n))^2 - (nonprime(n))^2.

Original entry on oeis.org

4, 8, 9, 13, 57, 88, 189, 217, 333, 616, 705, 1045, 1281, 1408, 1725, 2233, 2856, 3045, 3760, 4257, 4429, 5217, 5800, 6765, 8184, 8905, 9165, 9928, 10281, 11005, 14193, 15136, 16653, 17017, 19800, 20301, 22048, 23865, 24973, 26904, 28905, 29512, 33117
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 18 2009

Keywords

Examples

			a(1)=4-0^2=4. a(2)=9-1^2=8. a(3)=25-4^2=9. a(4)=49-6^2=13. a(5)=121-8^2=57.
		

Crossrefs

Programs

  • Mathematica
    A161753:= With[{nn = 2100}, Complement[Range[0, nn], Prime[Range[PrimePi[nn]]]]^2]; Table[Prime[n]^2 - A161753[[n]], {n, 1, 100}] (* G. C. Greubel, Oct 25 2018 *)

Formula

a(n) = A000040(n)^2 - A141468(n)^2 = A001248(n) - A161753(n).

Extensions

Definition condensed, 78 replaced by 88, 145 replaced by 217, 433 replaced by 333 etc. by R. J. Mathar, Jun 27 2009

A163121 (prime(n))^3-(nonprime(n))^3 .

Original entry on oeis.org

8, 26, 61, 127, 819, 1468, 3913, 5131, 9423, 21014, 25695, 44821, 60921, 70246, 93175, 135053, 189754, 209405, 281080, 335959, 362017, 460271, 535850, 665665, 869798, 983645, 1037855, 1165724, 1231029, 1368809, 1963199, 2156966, 2474017, 2575027
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jul 21 2009

Keywords

Comments

Cube of the n-th prime, A000040(n), minus cube of the n-th nonprime, A141468(n).

Examples

			a(1)=2^3-0^3=8. a(2)=3^3-1^2=26. a(3)=5^3-4^3=61. a(4)=7^3-6^3=127.
		

Crossrefs

Formula

a(n) = A030078(n)-A141468(n)^3 = A161671(n)*(A001248(n)+A000040(n)*A141468(n)+A161753(n)).

Extensions

Extended by R. J. Mathar, Jul 31 2009
Showing 1-3 of 3 results.