A210547 -id:A210547 - cp's OEIS frontend

A210546 Emirps whose products of digits are prime.

13, 17, 31, 71, 113, 311, 1151, 1511, 111211, 112111, 1111711, 1171111, 11111117, 11113111, 11131111, 71111111, 111111131, 131111111, 1111115111, 1115111111, 11111111113, 31111111111, 111111111111111131, 131111111111111111, 1111111111111111111111111511

Offset: 1

Lekraj Beedassy, Mar 22 2012

Chai Wah Wu, Table of n, a(n) for n = 1..66

Cf. A006567, A046703, A210547, A210548.

from _future_ import division
from sympy import isprime
A210546_list = []
for l in range(1,20):
    q = (10**l-1)//9
    for i in range(l):
        for p in [2,3,5,7]:
            r = q+(p-1)*10**i
            s, t = str(r), str(r)[::-1]
            if s != t and isprime(r) and isprime(int(t)):
                A210546_list.append(r) # Chai Wah Wu, Aug 15 2017

5 more terms from Alois P. Heinz, Mar 29 2012

A210548 Larger of emirp pairs whose members have prime digital products.

Original entry on oeis.org

31, 71, 311, 1511, 112111, 1171111, 11131111, 71111111, 131111111, 1115111111, 31111111111, 131111111111111111, 1151111111111111111111111111, 11111111111711111111111111111, 131111111111111111111111111111111111111

Offset: 1

Lekraj Beedassy, Mar 22 2012

Beyond the first two terms, a(n) is the intersection of A173596 and A046703.

Cf. A006567, A210546, A210547.

More terms from Alois P. Heinz, Mar 22 2012

A181931 Lesser of emirpimes pairs the product of whose members has prime digital sum.

Original entry on oeis.org

115, 205, 226, 289, 335, 497, 667, 718, 1027, 1057, 1079, 1135, 1141, 1154, 1195, 1234, 1243, 1247, 1286, 1315, 1322, 1343, 1357, 1379, 1387, 1402, 1415, 1466, 1469, 1502, 1513, 1514, 1538, 1658, 1679, 1691, 1703, 1765, 1769, 1774, 1817, 1843, 1882, 1927, 1937, 1942

Offset: 1

Jonathan Vos Post, Apr 02 2012

This is to A210547 (Lesser of emirp pairs whose members have prime digital products) as emirpimes A097393 are to emirps A006567 and as A007953 (digital sums) are to A007954 (digital products).

			The smallest emirpimes, 15, is not an element, because 15 * 51 = 765 and 7 + 6 + 5 = 18, which is composite.
a(1) = 115 because 115 * 511 = 58765 and 5+8+7+6+5 = 31 is prime.
a(2) = 205 because 205 * 502 = 102910 and 1+0+2+9+1+0 = 13 is prime.
a(3) = 226 because 226 * 622 = 140572 and 1+4+0+5+7+2 = 19 is prime.

Cf. A001358, A004086, A007953, A007954, A097393, A210547.

read("transforms");
# insert A097393 code here
isA181931 := proc(n)
    local R ;
    R := digrev(n) ;
    if n < R then
        if isA097393(n) then
            isprime(digsum(n*R)) ;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 1 to 2000 do
    if isA181931(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Apr 05 2012

{k in A097393, k < R(k), such that A007953(k * R(k)) is prime}, where R(k) = A004086(k).

More terms from Robert G. Wilson v, Apr 04 2012

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A210546 Emirps whose products of digits are prime.

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A210548 Larger of emirp pairs whose members have prime digital products.

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A181931 Lesser of emirpimes pairs the product of whose members has prime digital sum.

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