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.

A157492 Apply partial sum operator twice to sequence of squares of the first n primes.

Original entry on oeis.org

4, 17, 55, 142, 350, 727, 1393, 2420, 3976, 6373, 9731, 14458, 20866, 29123, 39589, 52864, 69620, 90097, 115063, 145070, 180406, 221983, 270449, 326836, 392632, 468629, 555235, 653290, 763226, 885931, 1024765, 1180760, 1355524, 1549609
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

Links

Crossrefs

Cf. A001223, A014148, A014150, A061789, A069482, A129701.
Partial sums of A024450.

Programs

  • Maple
    ListTools:-PartialSums(ListTools:-PartialSums([seq(ithprime(i)^2,i=1..100)])); # Robert Israel, May 14 2019
  • Mathematica
    s0=s1=0;lst={};Do[p=Prime[n];s0+=p^2;s1+=s0;AppendTo[lst,s1],{n,5!}];lst
Nest[Accumulate,Prime[Range[40]]^2,2] (* Harvey P. Dale, Jan 01 2020 *)

A157493 Apply partial sum operator thrice to sequence of squares of the first n primes.

Original entry on oeis.org

4, 21, 76, 218, 568, 1295, 2688, 5108, 9084, 15457, 25188, 39646, 60512, 89635, 129224, 182088, 251708, 341805, 456868, 601938, 782344, 1004327, 1274776, 1601612, 1994244, 2462873, 3018108, 3671398, 4434624, 5320555, 6345320
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

Crossrefs

Cf. A001223, A014148, A014150, A061789, A069482, A129701, A157492.

Programs

  • Mathematica
    s0=s1=s2=0; Table[s0+=Prime[n]^2; s1+=s0; s2+=s1, {n,100}]
Nest[Accumulate,Prime[Range[40]]^2,3]  (* Harvey P. Dale, Jan 27 2011 *)

A276963 a(n) = prime(n+1)^4 - prime(n)^4.

Original entry on oeis.org

65, 544, 1776, 12240, 13920, 54960, 46800, 149520, 427440, 216240, 950640, 951600, 593040, 1460880, 3010800, 4226880, 1728480, 6305280, 5260560, 2986560, 10551840, 8508240, 15283920, 25787040, 15531120, 8490480, 18528720, 10078560, 21889200, 97097280, 34355280, 57775440
Offset: 1

Views

Author

Bhushan Bade, Sep 22 2016

Keywords

Examples

			a(1) = 3^4 - 2^4 = 65.
a(2) = 5^4 - 3^4 = 544.

Crossrefs

Cf. A069482, A129701.

A157494 Primes in A014150.

Original entry on oeis.org

2, 1429, 32869, 3189059, 5157791, 62701339, 139181423, 296686879, 522304883, 5070516751, 6276844867, 7098350179, 8983996079, 9331926623, 21211375343, 31177858939, 34861039007, 38865340309, 39918757589, 62858815181
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

Crossrefs

Cf. A001223, A014148, A014150, A061789, A069482, A122382, A129701, A157492, A157493

Programs

  • Mathematica
    s0=s1=s2=0;lst={};Do[p=Prime[n];s0+=p;s1+=s0;s2+=s1;If[PrimeQ[s2],AppendTo[lst,s2]],{n,7!}];lst
Select[Nest[Accumulate[#]&,Prime[Range[700]],3],PrimeQ] (* Harvey P. Dale, Jul 11 2025 *)

A261464 a(n) = prime(n+2)^3 - prime(n+1)^2 + prime(n).

Original entry on oeis.org

118, 321, 1287, 2083, 4755, 6583, 11823, 23879, 28973, 49721, 67583, 77863, 102015, 146711, 202617, 223553, 297101, 353483, 384043, 487781, 565619, 698159, 904835, 1020981, 1082623, 1214535, 1283683, 1431123, 2035723, 2232075, 2554319, 2666981, 3288765
Offset: 1

Views

Author

Altug Alkan, Aug 20 2015

Keywords

Examples

			a(1) = 5^3 - 3^2 + 2 = 118.

Crossrefs

Cf. A136612, A069482, A129701.

Programs

  • Magma
    [NthPrime(n+2)^3-NthPrime(n+1)^2+NthPrime(n): n in [1.. 35]]; // Vincenzo Librandi, Aug 20 2015
  • Mathematica
    Table[Prime[n + 2]^3 - Prime[n + 1]^2 + Prime[n], {n, 60}] (* Vincenzo Librandi, Aug 20 2015 *)
  • PARI
    vector(40, n, prime(n+2)^3-prime(n+1)^2+prime(n)) \\ Michel Marcus, Aug 20 2015

Formula

a(n) = prime(n+2)^3 - prime(n+1)^2 + prime(n).

Extensions

More terms from Vincenzo Librandi, Aug 20 2015

A261465 a(n) = prime(n+1)^2 - prime(n).

Original entry on oeis.org

7, 22, 44, 114, 158, 276, 344, 510, 818, 932, 1338, 1644, 1808, 2166, 2762, 3428, 3662, 4428, 4974, 5258, 6168, 6810, 7838, 9320, 10104, 10508, 11346, 11774, 12660, 16016, 17034, 18638, 19184, 22062, 22652, 24498, 26412, 27726, 29762
Offset: 1

Views

Author

Altug Alkan, Aug 20 2015

Keywords

Examples

			a(2) = 5^2 - 3 = 22.

Crossrefs

Cf. A036689, A001223, A069482, A129701.

Programs

Formula

a(n) = A036689(n+1) + A001223(n). - Michel Marcus, Aug 21 2015 [Corrected by Georg Fischer, Dec 12 2022]
a(n) ~ n^2 log^2 n. - Charles R Greathouse IV, Aug 22 2015
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.