cp's OEIS Frontend

A227922 Numbers whose digits are prime and which retain this property when multiplied by some 1-digit prime (i.e., one of 2, 3, 5 or 7).

%I A227922 #34 Jan 05 2014 02:51:25
%S A227922 5,7,25,55,75,325,555,755,775,2525,2575,3225,3325,5325,5555,7525,7555,
%T A227922 7575,7775,25775,32225,33225,33325,53225,53325,55555,75325,75555,
%U A227922 75775,77525,77575,77775
%N A227922 Numbers whose digits are prime and which retain this property when multiplied by some 1-digit prime (i.e., one of 2, 3, 5 or 7).
%C A227922 Motivated by Gardner's puzzle, which reads: In the following calculation,
%C A227922 |   PPP
%C A227922 |  x PP
%C A227922 |------
%C A227922 |  PPPP
%C A227922 | PPPP
%C A227922 |------
%C A227922 | PPPPP
%C A227922 replace each P by some prime digit, to produce a correct calculation.
%D A227922 Martin Gardner, "The Unexpected Hanging and Other Mathematical Diversions", University of Chicago Press (November 1991), ISBN: 978-0226282565.
%H A227922 Charles R Greathouse IV, <a href="/A227922/b227922.txt">Table of n, a(n) for n = 1..1000</a>
%H A227922 "Mathematically Possible", <a href="http://www.facebook.com/photo.php?fbid=1407969406083700">PPP x PP = PPPPP</a>, on facebook.com.
%e A227922 a(1)=5 is in the sequence because 5x5=25 which has only prime digits.
%e A227922 a(2)=7 is in the sequence because 7x5=35 has only prime digits.
%e A227922 a(3)=25 is in the sequence because 25x3=75 has only prime digits.
%o A227922 (PARI) {(p(x)=Set(isprime(digits(x)))==[1]);for(x=2,1e5,p(x)&&forprime(q=2,9,p(x*q)&&!print1(x",")&&break))}
%o A227922 (PARI) conv(v)=subst(Pol(apply(k->[2,3,5,7][k+1],v)),'x,10)
%o A227922 isA046034(n)=!#setminus(Set(digits(n)),[2,3,5,7])
%o A227922 for(d=1,7,forstep(k=4^d+2,2*4^d-1,[1,3],n=conv(digits(k,4)[2..d+1]); if(vecmax(apply(isA046034, [2,3,5,7]*n)), print1(n", ")))) \\ _Charles R Greathouse IV_, Jan 05 2014
%Y A227922 A subsequence of A046034.
%K A227922 nonn,base
%O A227922 1,1
%A A227922 _M. F. Hasler_, Oct 12 2013