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 1-4 of 4 results.

A244914 Duplicate of A227126.

Original entry on oeis.org

2, 3, 5, 11, 17, 167, 193, 197, 433, 4111, 9173, 42929, 95279, 98897, 139409
Offset: 1

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Author

Keywords

A228021 Prime(k) such that 2^(k - 1) + prime(k) is also prime.

Original entry on oeis.org

2, 3, 29, 89, 251, 659, 937, 1307, 1453, 8179, 9391, 12097, 28499, 83969, 101209, 120739, 730993
Offset: 1

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Author

Juri-Stepan Gerasimov, Aug 03 2013

Keywords

Comments

The primes indices k are 1, 2, 10, 24, 54, 120, 159, 214, 231, 1027, 1161, 1447, 3100, 8188, 9695, 11363 ...
The corresponding primes 2^(k - 1) + prime(k) are 3, 5, 541, 8388697,...
a(18) > 2*10^6. - Michael S. Branicky, Apr 16 2025

Examples

			29 is in the sequence because 29 = prime(10) and 2^(10 - 1) + 29 = 512 + 29 = 541 is prime.
		

Crossrefs

Programs

  • Maple
    for i from 1 do
        p := ithprime(i) ;
        if isprime(p+2^(i-1)) then
           printf("%d,\n",p) ;
        end if;
    end do: # R. J. Mathar, Jul 12 2014
  • Mathematica
    p = 2; lst = {}; While[p < 730001, If[ PrimeQ[ 2^(PrimePi@ p-1) + p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Jul 09 2014 *)
  • PARI
    lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip-1)+p), print1(p, ", ")); ip++;);} \\ Michel Marcus, Jul 12 2014

Extensions

a(3) - a(9) from _Olivier Gérard_, Aug 01 2013
a(10) - a(15) from Robert G. Wilson v, Aug 01 2013
a(16) from Robert G. Wilson v, Jul 09 2014
a(17) from Michael S. Branicky, Apr 14 2025

A244913 Primes prime(k) such that 2^(k-1) - prime(k) is also prime.

Original entry on oeis.org

11, 13, 17, 19, 23, 37, 61, 233, 257, 1553, 2879, 4919, 6389, 7621, 8081, 35593, 37951, 96263, 206419, 596803, 1202837, 2837851
Offset: 1

Views

Author

Robert G. Wilson v, Jul 09 2014

Keywords

Comments

a(22) > 1211303. - J.W.L. (Jan) Eerland, Dec 08 2022
a(23) > 3000000. - Michael S. Branicky, Jun 03 2025

Crossrefs

Programs

  • Maple
    for i from 1 do
        p := ithprime(i) ;
        if isprime(2^(numtheory[pi](p-1))-p) then
            printf("%d,\n",p) ;
        end if;
    end do: # R. J. Mathar, Jul 11 2014
  • Mathematica
    p = 2; lst = {}; While[p < 800001, If[ PrimeQ[ 2^(PrimePi@ p-1) - p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst
    n=1;Monitor[Parallelize[While[True,If[PrimeQ[2^(PrimePi[Prime[n]-1])-Prime[n]],Print[Prime[n]]];n++];n],n] (* J.W.L. (Jan) Eerland, Dec 08 2022 *)
  • PARI
    is(n)=isprime(n) && isprime(2^primepi(n-1)-n) \\ Charles R Greathouse IV, Feb 25 2017

Formula

{p in A000040: 2^[A000720(p-1)]-p in A000040}. - R. J. Mathar, Jul 11 2014

Extensions

a(21) from J.W.L. (Jan) Eerland, Dec 08 2022
a(22) from Michael S. Branicky, Jun 02 2025

A244916 Primes prime(k) such that 2^(k+1) + prime(k) is also prime.

Original entry on oeis.org

3, 31, 71, 97, 107, 277, 307, 641, 907, 967, 1009, 1447, 3463, 3527, 7757, 8167, 250867, 279047, 1107791, 1176671, 1538399, 1594909, 2450017
Offset: 1

Views

Author

Robert G. Wilson v, Jul 09 2014

Keywords

Crossrefs

Programs

  • Maple
    for i from 1 do
            p := ithprime(i) ;
            if isprime(p+2^(i+1)) then
                    printf("%d,\n",p) ;
            end if;
    end do: # R. J. Mathar, Jul 12 2014
  • Mathematica
    p = 2; lst = {}; While[p < 900000, If[ PrimeQ[ 2^(PrimePi@ p +1) + p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst
  • PARI
    lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip+1)+p), print1(p, ", ")); ip++;);} \\ Michel Marcus, Jul 12 2014

Extensions

a(19)-a(23) from Michael S. Branicky, May 31 2025
Showing 1-4 of 4 results.