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

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

Author

Jonathan Vos Post, Apr 02 2012

Keywords

• nonn
• base
• easy

Comments

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).

Examples

			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.
		

Crossrefs

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

Programs

Maple

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

Formula

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

Extensions

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