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A326611 Numbers with exactly two distinct digits and divisible by both of these two digits. 3 12, 15, 24, 36, 48, 112, 115, 122, 144, 155, 212, 224, 244, 288, 336, 366, 424, 448, 488, 515, 636, 848, 1112, 1113, 1115, 1116, 1122, 1131, 1144, 1155, 1212, 1222, 1311, 1444, 1515, 1555, 1771, 1888, 2112, 2122, 2212, 2224, 2226, 2232, 2244, 2262, 2288, 2322 (list; graph; refs; listen; history; text; internal format) OFFSET 1,1 COMMENTS Intersection of A031955 and A034838. The first term whose two distinct digits are 7 and 9 is 77777779779, this is the largest of which (except the impossible digit pairs, such as 2 and 5), the second-largest of which is 8888889888, with two distinct digits 8 and 9. Digit pairs (d_1, d_2) the first term with digits d_1 and d_2 (1, 2) 12 (1, 3) 1113 (1, 4) 144 (1, 5) 15 (1, 6) 1116 (1, 7) 1771 (1, 8) 1888 (1, 9) 1111111119 (2, 3) 2232 (2, 4) 24 (2, 5) (none) (2, 6) 2226 (2, 7) 2772 (2, 8) 288 (2, 9) 2222222292 (3, 4) 3444 (3, 5) 3555 (3, 6) 36 (3, 7) 37737 (3, 8) 3888 (3, 9) 3339 (4, 5) (none) (4, 6) 4464 (4, 7) 44744 (4, 8) 48 (4, 9) 4444444944 (5, 6) (none) (5, 7) 5775 (5, 8) (none) (5, 9) 5555555595 (6, 7) 76776 (6, 8) 6888 (6, 9) 6696 (7, 8) 7888888 (7, 9) 77777779779 (8, 9) 8888889888 LINKS Richard N. Smith, Table of n, a(n) for n = 1..1298 (all terms <= 10^7) MATHEMATICA aQ[n_] := Length[(d = Union[IntegerDigits[n]])] == 2 && !MemberQ[d, 0] && And@@(Divisible[n, #] & /@ d); Select[Range[2400], aQ] (* Amiram Eldar, Jul 15 2019 *) PROG (PARI) isok(n) = {my(d = Set(digits(n))); if ((#d == 2) && vecmin(d), if ((n % d[1]) || (n % d[2]), return (0)); return (1); ); return (0); } \\ Michel Marcus, Jul 15 2019 CROSSREFS Cf. A031955, A034838. Sequence in context: A274550 A253235 A050480 * A290508 A063604 A124521 Adjacent sequences: A326608 A326609 A326610 * A326612 A326613 A326614 KEYWORD nonn,base,changed AUTHOR Richard N. Smith, Jul 14 2019 STATUS proposed