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A181931
Lesser of emirpimes pairs the product of whose members has prime digital sum.
0
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
1,1
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).
FORMULA
{a(n) = {k in A097393, k < R(k), such that A007953(k * R(k)) is prime} = {k in A097393 such that A007953(k * A004086(k)) is in A000040}.
EXAMPLE
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.
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
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Jonathan Vos Post, Apr 02 2012
EXTENSIONS
More terms from Robert G. Wilson v, Apr 04 2012
STATUS
approved