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.

A127435 Primes p such that (p-1)^2 + 1 is prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 37, 41, 67, 127, 131, 151, 157, 181, 211, 241, 251, 257, 271, 281, 307, 397, 401, 421, 431, 467, 491, 557, 571, 577, 647, 691, 701, 751, 761, 827, 907, 911, 937, 947, 967, 1061, 1097, 1151, 1277, 1291, 1307, 1321, 1367, 1567, 1571, 1861
Offset: 1

Views

Author

Lekraj Beedassy, Jan 14 2007

Keywords

Comments

Consists of 3 and a subsequence of A045349.
These are the primes of the form A067720(k)+1. - Michel Marcus, Nov 21 2020

Links

Crossrefs

For the associated primes, see A127436.
Cf. A045349, A067720.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | IsPrime((p^2-2*p+2))]; // Vincenzo Librandi, Jul 20 2025
  • Mathematica
    Select[Prime@Range[300], PrimeQ[(# - 1)^2 + 1] &] (* Ray Chandler, Jan 23 2007 *)
  • PARI
    listp(nn) = {forprime(p=2, nn, if (isprime((p-1)^2 + 1), print1(p, ", ")););} \\ Michel Marcus, Jun 08 2016

Formula

a(n) = sqrt(A127436(n)-1) + 1.

Extensions

Corrected and extended by Ray Chandler, Jan 23 2007

A157468 Primes of the form sqrt(p-1)-1, where p is a prime.

Original entry on oeis.org

3, 5, 13, 19, 23, 53, 73, 83, 89, 109, 149, 179, 223, 229, 239, 263, 269, 283, 313, 349, 383, 419, 439, 443, 463, 569, 593, 643, 653, 673, 739, 859, 863, 919, 929, 1009, 1069, 1093, 1123, 1289, 1319, 1373, 1409, 1429, 1433, 1439, 1459
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

Examples

			3 is in the sequence because 3 = sqrt(17 - 1) - 1, where 17 is prime.
5 is in the sequence because 5 = sqrt(37 - 1) - 1, where 37 is prime.

Links

Crossrefs

Cf. A070155, A127435, A127436, A157467.
Column k=1 of A238048 and A238086.

Programs

  • Mathematica
    Select[Sqrt[#-1]-1&/@Prime[Range[200000]],PrimeQ]  (* Harvey P. Dale, May 19 2012 *)

A157467 Primes of the form p^2 + 2*p + 2 where p is prime.

Original entry on oeis.org

17, 37, 197, 401, 577, 2917, 5477, 7057, 8101, 12101, 22501, 32401, 50177, 52901, 57601, 69697, 72901, 80657, 98597, 122501, 147457, 176401, 193601, 197137, 215297, 324901, 352837, 414737, 427717, 454277, 547601, 739601, 746497, 846401
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

Crossrefs

Cf. A127435, A127436.

Programs

  • Magma
    [a: p in PrimesUpTo(950) | IsPrime(a) where a is p^2+2*p+2]; // Vincenzo Librandi, Dec 20 2010
  • Mathematica
    lst={};Do[p=Prime[n];r=Sqrt[p-1]-1;If[PrimeQ[r],AppendTo[lst,p]],{n,4*8!}];lst
  • PARI
    forprime(p=2,1000,m=p^2+2*p+2;if(isprime(m),print1(m,", ")))

A157473 Primes p such that (p-2)^(1/3) -+ 2 are also primes.

Original entry on oeis.org

2, 127, 91127, 328511, 1157627, 2146691, 12326393, 125751503, 693154127, 751089431, 1033364333, 2102071043, 2222447627, 2893640627, 3314613773, 3951805943, 6591796877, 9063964127, 13464285941, 16406426423, 19880486831
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

Examples

			(127-2)^(1/3) - 2 = 3 and (127-2)^(1/3) + 2 = 7, so 127 is in the sequence.

Crossrefs

Cf. A127435, A127436, A157467, A157468.

Programs

  • Mathematica
    q=2;lst={};Do[p=Prime[n];r=(p-q)^(1/3)-q;u=(p-q)^(1/3)+q;If[PrimeQ[r]&&PrimeQ[u],AppendTo[lst,p]],{n,4*9!}];lst
lst = {}; p = 0; While[p < 2955, If[ PrimeQ[p - 2] && PrimeQ[p + 2] && PrimeQ[p^3 + 2], AppendTo[lst, p^3 + 2]]; p++ ]; lst (* Robert G. Wilson v, Mar 08 2009 *)
Select[Prime[Range[10^6]],AllTrue[Surd[#-2,3]+{2,-2},PrimeQ]&] (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Aug 31 2024 *)

Extensions

a(8)-a(21) from Robert G. Wilson v, Mar 08 2009
Showing 1-4 of 4 results.

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