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A366959 Numbers whose difference between the largest and smallest digits is equal to 2.

%I A366959 #23 Nov 11 2023 00:15:09
%S A366959 13,20,24,31,35,42,46,53,57,64,68,75,79,86,97,102,113,120,123,131,132,
%T A366959 133,200,201,202,210,213,220,224,231,234,242,243,244,311,312,313,321,
%U A366959 324,331,335,342,345,353,354,355,422,423,424,432,435,442,446,453,456,464,465,466
%N A366959 Numbers whose difference between the largest and smallest digits is equal to 2.
%C A366959 The number of n-digit terms of this sequence is (46*3^n - 93*2^n + 48)/6.
%H A366959 Robert Israel, <a href="/A366959/b366959.txt">Table of n, a(n) for n = 1..10000</a>
%p A366959 F:= proc(d) local L,i;
%p A366959    L:= select(t -> max(t) = 2 and min(t) = 0, map(convert,[$3^d..2*3^d-1],base,3));
%p A366959    L:= map(t -> add(t[-i-1]*10^(i-1),i=1..nops(t)-1),L);
%p A366959    L:= map(t -> seq(t+i*(10^d-1)/9,i=0..7), L);
%p A366959    op(sort(select(t -> t >= 10^(d-1), L)));
%p A366959 end proc:
%p A366959 F(2), F(3), F(4); # _Robert Israel_, Nov 10 2023
%t A366959 Select[Range[500],Max[d=IntegerDigits[#]]-Min[d]==2 &]
%o A366959 (Python)
%o A366959 def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 2
%o A366959 print([k for k in range(500) if ok(k)]) # _Michael S. Branicky_, Oct 30 2023
%o A366959 (Python)
%o A366959 from itertools import chain, count, islice, combinations_with_replacement
%o A366959 from sympy.utilities.iterables import multiset_permutations
%o A366959 def A366959_gen(): # generator of terms
%o A366959     return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for a in range(8) for c in combinations_with_replacement(range(a,a+3),l) for t in multiset_permutations((a,a+2)+c) if t[0]) for l in count(0))
%o A366959 A366959_list = list(islice(A366959_gen(),30)) # _Chai Wah Wu_, Nov 10 2023
%o A366959 (PARI) isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 2; \\ _Michel Marcus_, Nov 05 2023
%Y A366959 Cf. A037904.
%Y A366959 Cf. A010785 (difference = 0), A366958 (difference = 1), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8), A366966 (difference = 9).
%K A366959 nonn,base,easy
%O A366959 1,1
%A A366959 _Stefano Spezia_, Oct 30 2023