A380878 Numbers k such that k*(k+1) shares no decimal digits with k or k+1.
2, 3, 4, 5, 6, 7, 8, 15, 17, 18, 22, 24, 32, 33, 34, 37, 42, 43, 44, 45, 47, 48, 53, 54, 55, 56, 57, 58, 65, 66, 76, 77, 78, 83, 85, 92, 143, 144, 148, 154, 156, 165, 175, 188, 194, 195, 222, 232, 237, 242, 257, 265, 292, 294, 303, 307, 312, 313, 322, 332, 333, 334, 343, 344, 375, 377, 387, 392
Offset: 1
Examples
a(8) = 15 is a term because 15 * 16 = 240 and none of its digits 2, 4, 0 occur in 15 or 16. 16 is not a term because 16 * 17 = 272 contains the digit 7 which also occurs in 17.
References
- If k is a term, then at least one of k and k+1 is in A375211.
- Contains (10^k - 4)/3, (10^k - 1)/3, (10^k + 2)/3, (2*10^k - 5)/3 and (2*10^k - 2)/3 for each k >= 1.
Links
- Robert Israel, Table of n, a(n) for n = 1..5000
Crossrefs
Cf. A375211.
Programs
-
Maple
filter:= t -> (convert(convert(t,base,10),set) union convert(convert(t+1,base,10),set)) intersect convert(convert(t*(t+1),base,10),set) = {}: select(filter, [$1..1000]); -
Mathematica
A380878Q[k_] := Intersection[Join[IntegerDigits[k], IntegerDigits[k+1]], IntegerDigits[k*(k+1)]] == {}; Select[Range[500], A380878Q] (* Paolo Xausa, Feb 07 2025 *)
-
PARI
isok(k) = my(s=Set(digits(k)), t=Set(digits(k+1)), u=Set(digits(k*(k+1)))); (#setintersect(s, u)==0) && (#setintersect(t, u)==0); \\ Michel Marcus, Feb 07 2025