A231477 -id:A231477

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A262837

(3,7)-primes (defined in Comments).

+10
2

2, 3, 5, 7, 11, 19, 23, 29, 37, 43, 47, 53, 61, 67, 71, 79, 89, 103, 107, 127, 137, 149, 151, 173, 179, 191, 197, 211, 229, 233, 257, 271, 277, 281, 331, 337, 347, 373, 379, 383, 397, 401, 439, 443, 457, 467, 487, 499, 523, 547, 557, 571, 599, 607, 653, 673

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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).

LINKS

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

MATHEMATICA

{b1, b2} = {3, 7};

u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A231477 *)

v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262837 *)

w = Intersection[u, v]; (* A262838 *)

(* Peter J. C. Moses, Sep 27 2015 *)

CROSSREFS

Cf. A000040, A231477, A262838, A262829.

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Nov 09 2015

STATUS

approved

A262838

{3,7}-primes (defined in Comments).

+10
2

2, 3, 23, 47, 53, 61, 67, 71, 89, 127, 137, 191, 397, 443, 701, 1031, 1117, 1223, 1499, 1549, 1579, 1621, 1699, 1933, 1951, 2129, 2207, 2311, 2381, 2473, 2521, 2671, 2731, 2753, 2833, 3011, 3019, 3061, 3967, 4051, 4093, 4127, 4229, 4397, 4457, 4943, 5023

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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)).

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

MATHEMATICA

{b1, b2} = {3, 7};

u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A231477 *)

v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262837 *)

w = Intersection[u, v]; (* A262838 *)

(* Peter J. C. Moses, Sep 27 2015 *)

CROSSREFS

Cf. A000040, A231477, A262837, A262829.

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Nov 09 2015

STATUS

approved

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