A045331 -id:A045331 - cp's OEIS frontend

A160858 Primes p such that p^3-p^2-1 and p^3-p^2+1 are prime.

2, 3, 13, 541, 859, 1279, 1459, 1951, 2239, 2971, 3181, 4003, 4129, 6343, 7393, 8053, 9043, 9463, 10501, 10831, 12433, 14083, 14731, 15073, 15991, 16603, 17443, 17491, 17761, 18493, 19861, 20173, 20323, 20929, 21391, 22963, 23071

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 29 2009

nonn

			3^3-3^2=27-9=18-+1=primes

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Subset of A045331.

lst={};Do[p=Prime[n];a=p^2;b=p^3;c=b-a;If[PrimeQ[c-1]&&PrimeQ[c+1],AppendTo[lst,p]],{n,2*7!}];lst
Select[Prime[Range[3000]],AllTrue[#^3-#^2+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 20 2018 *)

forprime(p=2,1e6,if(isprime(p^3-p^2-1)&&isprime(p^3-p^2+1),print1(p",")))

Program, cross-reference, and editing by Charles R Greathouse IV, Nov 02 2009

A231476 Primes whose base-3 representation is also the base-6 representation of a prime.

Original entry on oeis.org

2, 7, 13, 19, 31, 151, 163, 211, 223, 229, 241, 271, 349, 367, 439, 601, 607, 613, 631, 643, 673, 727, 733, 859, 907, 937, 997, 1021, 1033, 1039, 1051, 1093, 1117, 1123, 1129, 1153, 1321, 1327, 1399, 1423, 1429, 1609, 1627, 1657, 1669, 1741, 1747, 1759, 1777, 1789, 1831, 1867, 1933, 1951, 1993, 1999

Offset: 1

M. F. Hasler, Jan 12 2014

This sequence is part of a two-dimensional array of sequences, given in the LINK, based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.

Subsequence of A045375 ⊂ A045331.

			7 = 21_3 and 21_6 = 13 are both prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Cf. A235469, A235265, A235266, A235473, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.

Select[Prime[Range[400]],PrimeQ[FromDigits[ IntegerDigits[#, 3], 6]] &] (* Harvey P. Dale, Sep 29 2016 *)

is(p,b=6,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b>c.

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A160858 Primes p such that p^3-p^2-1 and p^3-p^2+1 are prime.

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