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.

A108570 Squares of lesser of twin primes.

Original entry on oeis.org

9, 25, 121, 289, 841, 1681, 3481, 5041, 10201, 11449, 18769, 22201, 32041, 36481, 38809, 51529, 57121, 72361, 78961, 96721, 120409, 175561, 185761, 212521, 271441, 323761, 358801, 380689, 410881, 434281, 654481, 674041, 683929, 734449, 776161
Offset: 1

Views

Author

Giovanni Teofilatto, Jul 05 2005

Keywords

Comments

Squares of the form prime(n)*prime(n+1) - 2*prime(n).

Links

Crossrefs

Subsequence of A330477.
Cf. A001359, A108604.

Programs

  • Magma
    [p^2 : p in PrimesUpTo(1100)| IsPrime(p+2)]; // Vincenzo Librandi, Dec 23 2019
  • Maple
    ZL:=[]:for p from 1 to 950 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL),(p^2)]; fi; od; print(ZL); # Zerinvary Lajos, Mar 08 2007
  • Mathematica
    Select[First[#]Last[#]-2First[#]&/@Partition[Prime[Range[500]],2,1],IntegerQ[ Sqrt[#]]&] (* Harvey P. Dale, May 24 2011 *)
  • PARI
    p=2;forprime(q=3,, if(q-p==2, print1(p^2", ")); p=q) \\ Charles R Greathouse IV, Dec 16 2019

Extensions

Extended by Ray Chandler, Jul 10 2005
Name and comment swapped by Charles R Greathouse IV, Dec 16 2019

A111046 Difference between squares of twin prime pairs.

Original entry on oeis.org

16, 24, 48, 72, 120, 168, 240, 288, 408, 432, 552, 600, 720, 768, 792, 912, 960, 1080, 1128, 1248, 1392, 1680, 1728, 1848, 2088, 2280, 2400, 2472, 2568, 2640, 3240, 3288, 3312, 3432, 3528, 4080, 4128, 4200, 4248, 4368, 4608, 4920, 5112, 5160, 5208, 5280
Offset: 1

Views

Author

Giovanni Teofilatto, Oct 06 2005

Keywords

Comments

Except for the first term 16 = 4^2, a(n) is never a square.

Links

Crossrefs

Cf. A001359, A006512, A014574, A040040, A054735, A108570, A108604.

Programs

  • Haskell
    a111046 = (* 2) . a054735  -- Reinhard Zumkeller, Feb 10 2015
  • Maple
    ZL:=[]:for p from 1 to 1400 do if (isprime(p) and isprime(p+2)) then ZL:=[op(ZL),(((p+2)^2)-p^2)]; fi; od; print(ZL); # Zerinvary Lajos, Mar 08 2007
  • Mathematica
    Select[Table[Prime[n] + 1, {n, 220}], PrimeQ[ # + 1] &] *4 (* Ray Chandler, Oct 12 2005 *)
4+4#&/@Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]]==2&] [[All,1]] (* Harvey P. Dale, Apr 12 2018 *)

Formula

a(n) = A006512(n)^2 - A001359(n)^2 = A108604(n) - A108570(n) = 2*A054735(n) = 4*A014574(n) = 8*A040040(n).

Extensions

Edited and extended by Ray Chandler, Oct 12 2005

A110013 Squares of the form 4p + 5, where p is a prime.

Original entry on oeis.org

25, 49, 81, 121, 169, 289, 361, 441, 529, 729, 961, 1089, 1521, 1681, 1849, 2401, 2809, 3249, 3721, 3969, 5041, 5929, 6241, 6889, 7921, 8281, 8649, 9409, 10201, 11449, 11881, 12321, 12769, 14161, 14641, 16641, 17161, 17689, 18769, 19881, 23409
Offset: 1

Views

Author

Giovanni Teofilatto, Sep 03 2005

Keywords

Comments

The sequence contain all squares of greater of twin primes.

Links

Crossrefs

Cf. A002327, A002328, A088502.
Cf. A108604.

Programs

  • Mathematica
    Select[4#+5&/@Prime[Range[900]],IntegerQ[Sqrt[#]]&]  (* Harvey P. Dale, Jan 29 2011 *)

Formula

a(n) = 4*A002327(n) + 5 = A088502(n)^2.

Extensions

Corrected and extended by Ray Chandler, Sep 04 2005

A110484 Squares of the form p*q + p + q + 2, where p and q are primes.

Original entry on oeis.org

25, 49, 81, 121, 169, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2209, 2401, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 5041, 5329, 5929, 6241, 6889, 7225, 7921, 8281, 8649, 9025, 9409, 10201, 10609, 11449, 11881
Offset: 1

Views

Author

Giovanni Teofilatto, Sep 10 2005

Keywords

Comments

Includes A108604 squares of greater twin primes and A110013 squares of form 4p+5 where p is prime (q=3).

Crossrefs

Cf. A108604, A110013, A110487.

Extensions

Edited by Ray Chandler, Sep 13 2005

A362941 Numbers of the form (p+1)*(p+3) where (p,p+2) is a twin prime pair (cf. A001359).

Original entry on oeis.org

24, 48, 168, 360, 960, 1848, 3720, 5328, 10608, 11880, 19320, 22800, 32760, 37248, 39600, 52440, 58080, 73440, 80088, 97968, 121800, 177240, 187488, 214368, 273528, 326040, 361200, 383160, 413448, 436920, 657720, 677328, 687240, 737880, 779688, 1042440, 1067088, 1104600
Offset: 1

Views

Author

N. J. A. Sloane, Sep 10 2023, following a suggestion from Jean-Claude Babois

Keywords

Links

Crossrefs

Cf. A001359, A108604.

Programs

  • Mathematica
    ((# + 1)*(# + 3)) & /@ Select[Prime[Range[200]], PrimeQ[# + 2] &] (* Amiram Eldar, Sep 10 2023 *)

Formula

a(n) = A108604(n) - 1. - Amiram Eldar, Sep 10 2023
Showing 1-5 of 5 results.

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

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