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.

A088878 Prime numbers p such that 3p - 2 is a prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 23, 37, 43, 47, 53, 61, 67, 71, 103, 113, 127, 137, 163, 167, 181, 191, 193, 211, 251, 257, 263, 271, 277, 293, 307, 313, 331, 337, 347, 373, 401, 431, 433, 443, 461, 467, 487, 491, 523, 541, 557, 587, 593, 601, 673, 677, 727, 751, 757, 761
Offset: 1

Views

Author

Giovanni Teofilatto, Nov 27 2003

Keywords

Comments

Indices of semiprime octagonal numbers. - Jonathan Vos Post, Feb 16 2006
Daughter primes of order 1. - Artur Jasinski, Dec 12 2007
A010051(3*a(n)-2) = 1. - Reinhard Zumkeller, Jul 02 2015

Examples

			For p = 3, 3p - 2 = 7;
for p = 523, 3p - 2 = 1567.

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997

Links

Crossrefs

Cf. A000040, A000567, A001222, A001358, A091179, A091180, A091181, A136019, A136020, A153183, A153184.
Cf. A010051, A063908, A172287.
Cf. A259730.

Programs

  • Haskell
    a088878 n = a088878_list !! (n-1)
a088878_list = filter ((== 1) . a010051' . subtract 2 . (* 3)) a000040_list
-- Reinhard Zumkeller, Jul 02 2015
  • Magma
    [ p: p in PrimesUpTo(770) | IsPrime(3*p-2) ]; // Klaus Brockhaus, Dec 21 2008
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[3*p-2],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 22 2008 *)
n = 1; a = {}; Do[If[PrimeQ[(Prime[k] + 2n)/(2n + 1)], AppendTo[a, (Prime[k] + 2n)/(2n + 1)]], {k, 1, 500}]; a (* Artur Jasinski, Dec 12 2007 *)
Select[Prime[Range[150]],PrimeQ[3#-2]&] (* Harvey P. Dale, Feb 27 2024 *)
  • PARI
    list(lim)=select(p->isprime(3*p-2),primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011

Extensions

Corrected and extended by Ray Chandler, Dec 27 2003
Entry revised by N. J. A. Sloane, Nov 28 2006, Jul 08 2010

A063908 Numbers k such that k and 2*k-3 are primes.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 23, 31, 37, 41, 43, 53, 67, 71, 83, 97, 101, 107, 113, 127, 137, 157, 167, 181, 191, 193, 211, 223, 233, 241, 251, 263, 283, 311, 317, 331, 347, 373, 421, 431, 433, 443, 457, 461, 487, 521, 547, 563, 577, 587, 613, 617, 631, 641, 643, 647
Offset: 1

Views

Author

N. J. A. Sloane, Aug 31 2001

Keywords

Comments

If p is in this sequence then the products of positive powers of 3, p and 2p-3 are entries in A086486. - Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003
Median prime of AP3's starting at 3, i.e., triples of primes (3,p,q) in arithmetic progression. - M. F. Hasler, Sep 24 2009
a(n) = sum of the coprimes(p) mod (p+1). - J. M. Bergot, Nov 13 2014
A010051(2*a(n)-3) = 1. - Reinhard Zumkeller, Jul 02 2015
A098090 INTERSECT A000040. - R. J. Mathar, Mar 23 2017

Examples

			From _K. D. Bajpai_, Nov 29 2019: (Start)
a(5) = 13 is prime and 2*13 - 3 = 23 is also prime.
a(6) = 17 is prime and 2*17 - 3 = 31 is also prime.
(End)

Links

Crossrefs

Cf. A005382.
Cf. A000040, A010051, A088878, A172287.
Cf. A259730.

Programs

  • Haskell
    a063908 n = a063908_list !! (n-1)
a063908_list = filter
   ((== 1) . a010051' . (subtract 3) . (* 2)) a000040_list
-- Reinhard Zumkeller, Jul 02 2015
  • Magma
    [n : n in [0..700] | IsPrime(n) and IsPrime(2*n-3)]; // Vincenzo Librandi, Nov 14 2014
  • Maple
    select(k -> andmap(isprime, [k, 2*k-3]), [seq(k, k=1.. 10^4)]); # K. D. Bajpai, Nov 29 2019
  • Mathematica
    Select[Prime[Range[6! ]],PrimeQ[2*#-3]&] (* Vladimir Joseph Stephan Orlovsky, Nov 17 2009 *)
  • PARI
    { n=0; p=1; for (m=1, 10^9, p=nextprime(p+1); if (isprime(2*p - 3), write("b063908.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 02 2009
  • PARI
    forprime( p=1,default(primelimit), isprime(2*p-3) && print1(p",")) \\ M. F. Hasler, Sep 24 2009

Formula

a(n) = A241817(n)/2. - Wesley Ivan Hurt, Apr 08 2018

A259730 Primes p such that both 2*p - 3 and 3*p - 2 are prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 23, 37, 43, 53, 67, 71, 113, 127, 137, 167, 181, 191, 193, 211, 251, 263, 331, 347, 373, 431, 433, 443, 461, 487, 587, 727, 751, 757, 907, 991, 1021, 1091, 1103, 1171, 1187, 1213, 1231, 1297, 1367, 1453, 1483, 1597, 1637, 1663, 1667, 1733
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 05 2015

Keywords

Comments

A010051(2*a(n) - 3) * A010051(3*a(n) - 2) = 1;
A259758(n) = (2*a(n) - 3) * (3*a(n) - 2).
Except for a(1)=3 this is the same sequence as primes p such that A288814(3*p) - A288814(2*p) = 5. - David James Sycamore, Jul 22 2017
Furthermore, (A288814(3*p)*A288814(2*p))/6 belongs to A259758. - David James Sycamore, Jul 23 2017

Links

Crossrefs

Intersection of A063908 and A088878; A172287, A259758.
Cf. A288814, A259758.

Programs

  • Haskell
    import Data.List.Ordered (isect)
a259730 n = a259730_list !! (n-1)
a259730_list = a063908_list `isect` a088878_list
  • Mathematica
    Select[Prime@ Range@ 270, Times @@ Boole@ Map[PrimeQ, {2 # - 3, 3 # - 2}] > 0 &] (* Michael De Vlieger, Jul 22 2017 *)
Select[Prime[Range[300]],AllTrue[{2#-3,3#-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 08 2020 *)
  • PARI
    lista(nn) = forprime(p=3, nn, if(isprime(2*p-3) && isprime(3*p-2), print1(p, ", "))); \\ Altug Alkan, Jul 22 2017

A337480 Numbers k such that exactly one of 6*k + 5 and 12*k + 5 is prime.

Original entry on oeis.org

6, 12, 13, 17, 18, 19, 23, 26, 27, 28, 31, 33, 39, 41, 44, 47, 48, 49, 52, 53, 54, 56, 57, 59, 67, 68, 69, 74, 76, 78, 83, 86, 87, 88, 91, 93, 94, 97, 101, 109, 112, 114, 116, 117, 124, 126, 128, 129, 132, 133, 137, 139, 141, 144, 146, 147, 151, 154, 159, 161
Offset: 1

Views

Author

K. D. Bajpai, Aug 28 2020

Keywords

Examples

			a(5) = 18 is a term because 6*18 + 5 = 113 is prime; but 12*18 + 5 = 221 = (13*17) is a composite number.
a(8) = 26 is a term because 6*26 + 5 = 161 = (7*23) is a composite number; but 12*26 + 5 = 317 is prime.

Links

Crossrefs

Cf. A063913, A145487, A145490, A172287.

Programs

  • Maple
    A337480:=k->`if`(isprime(6*k+5) xor isprime(12*k+5),k, NULL): seq(A337480(k), k=1..1000);
  • Mathematica
    Select[Range[0, 250], Xor[PrimeQ[6 # + 5], PrimeQ[12 # + 5]] &]
  • PARI
    for(k=1, 1000, if (bitxor(isprime(6*k+5), isprime(12*k+5)), print1(k, ", ")));

A172365 List of primes p1, p2 and p3 such that 3*p1 - 2 = 2*p2 - 3 = p3.

Original entry on oeis.org

3, 5, 7, 7, 11, 19, 11, 17, 31, 47, 71, 139, 67, 101, 199, 71, 107, 211, 127, 191, 379, 167, 251, 499, 211, 317, 631, 307, 461, 919, 347, 521, 1039, 431, 647, 1291, 467, 701, 1399, 587, 881, 1759, 727, 1091, 2179, 907, 1361, 2719, 911, 1367, 2731, 991, 1487, 2971
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 01 2010

Keywords

Examples

			a(1) = 3 = p1, a(2) = 5 = p2, a(3) = 7 = p3 because 3*3 - 2 = 2*5 - 3 = 7;
a(4) = 11 = p1, a(5) = 17 = p2, a(6) = 31 = p3 because 3*11 - 2 = 2*17 - 3 = 31.

Links

Crossrefs

Cf. A000040, A172287, A172888.

Programs

  • Maple
    for n from 1 to 500 do p1 := ithprime(n) ; p3 := 3*p1-2 ; if isprime(p3) then p2 := (p3+3)/2 ; if isprime(p2) then printf("%d,%d,%d,",p1,p2,p3) ; end if; end if; end do: # R. J. Mathar, May 02 2010
  • Mathematica
    Flatten[Select[Tuples[Prime[Range[450]],{3}],3First[#]-2==2#[[2]]-3== Last[#]&]] (* Harvey P. Dale, Jun 02 2011 *)

Extensions

Corrected (triples 7,11,19 and 167,251,499 inserted) and extended by R. J. Mathar, May 02 2010
Showing 1-5 of 5 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.