A157467 -id:A157467 - cp's OEIS frontend

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

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

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

nonn

			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.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A070155, A127435, A127436, A157467.

Column k=1 of A238048 and A238086.

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

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

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

nonn

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

Cf. A127435, A127436, A157467, A157468.

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 *)

a(8)-a(21) from Robert G. Wilson v, Mar 08 2009

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica