A366959 - OEIS

%I #23 Nov 11 2023 00:15:09

%S 13,20,24,31,35,42,46,53,57,64,68,75,79,86,97,102,113,120,123,131,132,

%T 133,200,201,202,210,213,220,224,231,234,242,243,244,311,312,313,321,

%U 324,331,335,342,345,353,354,355,422,423,424,432,435,442,446,453,456,464,465,466

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

%C The number of n-digit terms of this sequence is (46*3^n - 93*2^n + 48)/6.

%H Robert Israel, <a href="/A366959/b366959.txt">Table of n, a(n) for n = 1..10000</a>

%p F:= proc(d) local L,i;

%p    L:= select(t -> max(t) = 2 and min(t) = 0, map(convert,[$3^d..2*3^d-1],base,3));

%p    L:= map(t -> add(t[-i-1]*10^(i-1),i=1..nops(t)-1),L);

%p    L:= map(t -> seq(t+i*(10^d-1)/9,i=0..7), L);

%p    op(sort(select(t -> t >= 10^(d-1), L)));

%p end proc:

%p F(2), F(3), F(4); # _Robert Israel_, Nov 10 2023

%t Select[Range[500],Max[d=IntegerDigits[#]]-Min[d]==2 &]

%o (Python)

%o def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 2

%o print([k for k in range(500) if ok(k)]) # _Michael S. Branicky_, Oct 30 2023

%o (Python)

%o from itertools import chain, count, islice, combinations_with_replacement

%o from sympy.utilities.iterables import multiset_permutations

%o def A366959_gen(): # generator of terms

%o     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_list = list(islice(A366959_gen(),30)) # _Chai Wah Wu_, Nov 10 2023

%o (PARI) isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 2; \\ _Michel Marcus_, Nov 05 2023

%Y Cf. A037904.

%Y 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 nonn,base,easy

%O 1,1

%A _Stefano Spezia_, Oct 30 2023