A065723 - OEIS

%I #16 Mar 05 2022 11:08:42

%S 2,3,13,23,41,71,83,101,163,191,211,281,283,311,331,463,503,571,613,

%T 653,701,743,823,863,881,983,1091,1213,1231,1283,1301,1373,1381,1423,

%U 1471,1493,1531,1543,1621,1741,1783,1861,1873,1931,2063,2203,2213,2221

%N Primes p such that the decimal expansion of its base-5 conversion is also prime.

%C In general rebase notation (Marc LeBrun): p5 = (5) [p] (10).

%H Harry J. Smith, <a href="/A065723/b065723.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%t Select[Prime[Range[400]],PrimeQ[FromDigits[IntegerDigits[#,5]]]&] (* _Harvey P. Dale_, Mar 28 2015 *)

%o (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

%Y Cf. A065720 up to A065727, A065361.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 15 2001