A235635 -id:A235635 - cp's OEIS frontend

A235627 Primes whose base-7 representation also is the base-5 representation of a prime.

2, 3, 7, 17, 23, 31, 53, 71, 73, 79, 101, 109, 113, 127, 151, 157, 197, 199, 359, 401, 409, 449, 463, 521, 541, 557, 743, 863, 1033, 1039, 1103, 1151, 1193, 1229, 1451, 1487, 1499, 1543, 2423, 2521, 2549, 2621, 2753, 2857, 2909, 2957, 3089, 3257, 3313, 3511, 3529, 3593

Offset: 1

M. F. Hasler, Jan 13 2014

This sequence is part of the two-dimensional array of sequences 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.

			Both 17 = 23_7 and 23_5 = 13 are prime.

Robert Price, Table of n, a(n) for n = 1..13736
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Cf. A235635, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

is(p,b=5,c=7)=vecmax(d=digits(p,c))

forprime(p=1,3e3,is(p,7,5)&&print1(vector(#d=digits(p,5),i,7^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,5,7)

A262839 (5,7)-primes (defined in Comments).

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 23, 31, 41, 43, 53, 71, 73, 79, 97, 101, 109, 113, 127, 137, 151, 157, 181, 191, 193, 197, 199, 233, 239, 251, 263, 277, 281, 311, 317, 337, 349, 359, 379, 401, 409, 431, 433, 449, 461, 463, 503, 521, 541, 557, 613, 617, 631, 643, 647

Offset: 1

Clark Kimberling, Nov 09 2015

Let V = (b(1), b(2), ..., b(k)), where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p a V-prime if the digits of p in base b(1) spell a prime in each of the bases b(2), ..., b(k).

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A000040, A235635, A262840, A262829.

{b1, b2} = {5, 7};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &];  (* A235635 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262839 *)
w = Intersection[u, v]; (* A262840 *)
(* Peter J. C. Moses, Sep 27 2015 *)

A262840 {5,7}-primes (defined in Comments).

Original entry on oeis.org

2, 3, 5, 13, 17, 23, 41, 43, 53, 71, 79, 101, 137, 157, 181, 191, 239, 281, 379, 463, 743, 839, 863, 967, 1151, 1171, 1303, 1367, 1663, 1721, 2083, 2251, 2297, 2351, 2621, 2659, 2957, 2999, 3257, 3343, 3373, 3511, 3607, 3767, 3863, 3877, 3907, 4217, 4447

Offset: 1

Clark Kimberling, Nov 09 2015

Let S = {b(1), b(2), ..., b(k)}, where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p an S-prime if the digits of p in base b(i) spell a prime in each of the bases b(j) in S, for i = 1..k. Equivalently, p is an S-prime if p is a strong-V prime (defined at A262729) for every permutation of the vector V = (b(1), b(2), ..., b(k)).

Clark Kimberling, Table of n, a(n) for n = 1..5000

Cf. A000040, A235635, A262839, A262829.

{b1, b2} = {5, 7};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &];  (* A235635 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262839 *)
w = Intersection[u, v]; (* A262840 *)
(* Peter J. C. Moses, Sep 27 2015 *)

cp's OEIS Frontend

A235627 Primes whose base-7 representation also is the base-5 representation of a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

PARI

A262839 (5,7)-primes (defined in Comments).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A262840 {5,7}-primes (defined in Comments).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica