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A262728 (2,3,5,7)-primes (see comments for precise definition). 4
2, 173, 181, 233, 443, 877, 967, 1373, 1831, 4001, 4231, 4663, 8191, 8753, 9043, 10333, 10631, 13537, 14591, 16931, 18211, 25411, 32707, 32843, 33637, 37573, 54773, 56167, 63853, 64513, 78101, 84131, 100207, 102667, 106087, 112571, 113153, 133087, 149531 (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..1000

EXAMPLE

Consider the number a(2) = 173:

in base 2, a(2) = 10101101, which is the prime 172;

in base 3, 10101101 is the prime 2467;

in base 5, 10101101 is the prime 81401;

in base 7, 10101101 is the prime 840743

MATHEMATICA

{b1, b2, b3, b4} = {2, 3, 5, 7}; z = 15000;

u = Select[Prime[Range[z]],

PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &&

PrimeQ[FromDigits[IntegerDigits[#, b1], b3]] &&

PrimeQ[FromDigits[IntegerDigits[#, b1], b4]] &]

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

CROSSREFS

Cf. A000040, A262729.

Sequence in context: A209607 A243230 A051030 * A139935 A281958 A172231

Adjacent sequences:  A262725 A262726 A262727 * A262729 A262730 A262731

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Oct 02 2015

STATUS

approved

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Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.