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

1,1

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.

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.

Example

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.

Prog

(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

Crossrefs

A subsequence of A046034.

Sequence in context: A018697 A018319 A100095 * A179782 A013626 A067701

Adjacent sequences: A227919 A227920 A227921 * A227923 A227924 A227925

Keyword

nonn,base

Author

M. F. Hasler, Oct 12 2013

Status

approved