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.

A214627 Primes in A161671.

Original entry on oeis.org

2, 3, 7, 19, 29, 43, 47, 71, 83, 101, 113, 193, 197, 229, 241, 271, 283, 293, 311, 347, 383, 439, 457, 463, 491, 499, 523, 587, 619, 643, 683, 733, 797, 827, 857, 863, 919, 991, 1021, 1031, 1091, 1151, 1187, 1289, 1367, 1549, 1567, 1619, 1637, 1693, 1697, 1733, 1741, 1811, 1867, 1871, 1907
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 08 2012

Keywords

Links

Crossrefs

Cf. A141468, A161671, A220220.

Programs

  • Maple
    isA214627 := proc(n)
        if isprime(n) then
                for j from 1 do
                        if A161671(j) = n then
                                return true;
                        elif j >7 and A161671(j) > n then
                                return false;
                        end if;
                end do:
        else
                false;
        end if;
end proc:
for n from 2 to 2000 do
        if isA214627(n) then
                printf("%d,",n) ;
        end if;
end do; # R. J. Mathar, Aug 09 2012
  • Mathematica
    f[n_] := FixedPoint[n + PrimePi@ # &, n + PrimePi@ n]; Union@ Reap[Do[If[PrimeQ[#], Sow[#]] &[Prime[i] - f[i - 1] ], {i, 350}] ][[-1, -1]] (* Michael De Vlieger, Mar 22 2022, after Robert G. Wilson v at A141468 *)

Formula

A161671 INTERSECT A000040.

A220220 Primes p of the form p = A161671(k) = A161671(k+1).

Original entry on oeis.org

2, 7, 43, 311, 491, 827, 1367, 1693, 1733, 1741, 2089, 2239, 2927, 3343, 5231, 5743, 9319, 9521, 11177, 12611, 13249, 15511, 16661, 17989, 24083, 24611, 25679, 25841, 28723, 37861, 39199, 46663, 47279, 51659, 53281, 58031, 58309, 58549, 59723, 64091, 68041, 70051, 70913, 71261
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 07 2012

Keywords

Comments

There are also composites m = A161671(k) = A161671(k+1). An example is 65 = A161671(26) = A161671(27). - Michael De Vlieger, Mar 22 2022

Examples

			The prime 2 is in the sequence because 2 = A161671(1) = A161671(2).

Links

Crossrefs

Cf. A141468, A161671, A214627.

Programs

  • Mathematica
    f[n_] := FixedPoint[n + PrimePi@ # &, n + PrimePi@ n]; Reap[Do[(If[PrimeQ[#] && # == j, Sow[#]]; j = #) &[Prime[i] - f[i - 1] ], {i, 8500}] ][[-1, -1]] (* Michael De Vlieger, Mar 22 2022, after Robert G. Wilson v at A141468 *)

A161778 The A161671(n)-th partial sum of A161671.

Original entry on oeis.org

4, 4, 2, 2, 5, 6, 20, 20, 36, 127, 152, 290, 376, 423, 590, 857, 1279, 1379, 1928, 2308, 2308, 2859, 3339, 4200, 5579, 6252, 6252, 6968, 7223, 7738, 11232, 12206, 13913, 13913, 17338, 17753, 19914, 22191, 23130, 25561, 28102, 28625, 33642, 33642, 34814
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 19 2009

Keywords

Examples

			a(1) = A163116(A161671(1)) = A163116(2) = 4.
a(2) = A163116(A161671(2)) = A163116(2) = 4.
a(5) = A163116(A161671(5)) = A163116(3) = 5.

Crossrefs

Cf. A000040, A141468, A161671.

Programs

  • Maple
    A141468 := proc(n) option remember ; 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:
A161671 := proc(n) ithprime(n)-A141468(n) ; end:
A161778 := proc(n) add( A161671(j),j=1..A161671(n)) ; end: seq(A161778(n),n=1..90) ; # R. J. Mathar, Oct 04 2009

Formula

a(n) = Sum_{j=1..A161671(n)} A161671(j) = A163116(A161671(n)).

Extensions

Edited, corrected from a(15) on, and extended by R. J. Mathar, Oct 04 2009

A163116 Partial sums of A161671.

Original entry on oeis.org

2, 4, 5, 6, 9, 13, 20, 27, 36, 50, 65, 84, 105, 127, 152, 181, 215, 250, 290, 333, 376, 423, 473, 528, 590, 655, 720, 788, 857, 928, 1011, 1097, 1188, 1279, 1379, 1480, 1586, 1697, 1810, 1928, 2051, 2175, 2308, 2441, 2576, 2712
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jul 21 2009

Keywords

Comments

The n-th partial sum of the primes minus the n-th partial sum of the nonprimes.

Examples

			a(1) = A161671(1) = 2.
a(2) = a(1) + A161671(2) = 2 + 2 = 4.
a(3) = a(2) + A161671(3) = 4 + 1 = 5.

Crossrefs

Cf. A000040, A141468, A161671.

Formula

a(n) = A007504(n) - A051349(n-1). - R. J. Mathar, Jul 31 2009

Extensions

Corrected from a(9) on by R. J. Mathar, Jul 31 2009

A168563 a(n) = (n-th prime > 3) minus (n-th composite number).

Original entry on oeis.org

1, 1, 3, 4, 7, 7, 9, 14, 15, 19, 21, 22, 25, 29, 34, 35, 40, 43, 43, 47, 50, 55, 62, 65, 65, 68, 69, 71, 83, 86, 91, 91, 100, 101, 106, 111, 113, 118, 123, 124, 133, 133, 135, 136, 147, 158, 161, 161, 164, 169, 169, 177, 182, 187, 192, 193, 197, 200, 201, 209, 222, 225, 226
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 29 2009

Keywords

Links

Crossrefs

Cf. A161671.

Programs

  • Mathematica
    Module[{nn=100,pr,cmp},cmp=Select[Range[nn],CompositeQ];pr=Prime[ Range[ 3, Length[cmp]+2]];pr-cmp] (* Harvey P. Dale, May 28 2015 *)

Formula

a(n) = prime(n+2)-composite(n) = A161671(n+2).

Extensions

Edited by Charles R Greathouse IV, Mar 25 2010

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

Cf. A000040, A030078, A141468, A161757.

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 1-6 of 6 results.

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