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A065723 Primes p such that the decimal expansion of its base-5 conversion is also prime. 4
2, 3, 13, 23, 41, 71, 83, 101, 163, 191, 211, 281, 283, 311, 331, 463, 503, 571, 613, 653, 701, 743, 823, 863, 881, 983, 1091, 1213, 1231, 1283, 1301, 1373, 1381, 1423, 1471, 1493, 1531, 1543, 1621, 1741, 1783, 1861, 1873, 1931, 2063, 2203, 2213, 2221 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In general rebase notation (Marc LeBrun): p(n) = (5) [p] (10).

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

E.g., 2213_10 = 32323_5 is prime, and so is 32323_10.

MATHEMATICA

Select[ Range[2250], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 5]]] & ]

Select[Prime[Range[400]], PrimeQ[FromDigits[IntegerDigits[#, 5]]]&] (* Harvey P. Dale, Mar 28 2015 *)

PROG

(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 5); if (isprime(b), write("b065723.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 27 2009

CROSSREFS

Cf. A065720 up to A065727, A065361.

Sequence in context: A133201 A215302 A103150 * A215134 A177746 A024779

Adjacent sequences:  A065720 A065721 A065722 * A065724 A065725 A065726

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Nov 15 2001

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)