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).

5, 7, 25, 55, 75, 325, 555, 755, 775, 2525, 2575, 3225, 3325, 5325, 5555, 7525, 7555, 7575, 7775, 25775, 32225, 33225, 33325, 53225, 53325, 55555, 75325, 75555, 75775, 77525, 77575, 77775

Offset: 1

Author

M. F. Hasler, Oct 12 2013

Keywords

• nonn
• base

Comments

Motivated by Gardner's puzzle, which reads: In the following calculation,

| PPP

| x PP

|------

| PPPP

| PPPP

|------

| PPPPP

replace each P by some prime digit, to produce a correct calculation.

Examples

			a(1)=5 is in the sequence because 5x5=25 which has only prime digits.
a(2)=7 is in the sequence because 7x5=35 has only prime digits.
a(3)=25 is in the sequence because 25x3=75 has only prime digits.
		

References

• Martin Gardner, "The Unexpected Hanging and Other Mathematical Diversions", University of Chicago Press (November 1991), ISBN: 978-0226282565.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
• "Mathematically Possible", PPP x PP = PPPPP, on facebook.com.

Crossrefs

A subsequence of A046034.

Programs

PARI

{(p(x)=Set(isprime(digits(x)))==[1]);for(x=2,1e5,p(x)&&forprime(q=2,9,p(x*q)&&!print1(x",")&&break))}

PARI

conv(v)=subst(Pol(apply(k->[2,3,5,7][k+1],v)),'x,10)
isA046034(n)=!#setminus(Set(digits(n)),[2,3,5,7])
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