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A203565
Numbers that contain the product of any two adjacent digits as a substring.
11
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 126, 130, 131, 140, 141, 150, 151
OFFSET
1,3
COMMENTS
Inspired by the problem restricted to pandigital numbers suggested by E. Angelini (cf. link).
E. Angelini observes that up to a(86) this is the same as "Numbers that contain the product of (all) their digits as a substring" (cf. A227510 for the zeroless terms); then 212 is here but not there, and 236 is there and not here. - M. F. Hasler, Oct 14 2014
LINKS
E. Angelini, 10 different digits, 9 products, seqfan list, Jan 03 2012.
EXAMPLE
Any number having no two adjacent digits larger than 1 is trivially in the sequence.
The smallest nontrivial example is the number 126, which is in the sequence since 1*2=2 and 2*6=12 are both substrings of "126".
MAPLE
filter:= proc(n)
local L, S, i;
S:= convert(n, string);
for i from 1 to length(S)-1 do
if StringTools:-Search(convert(parse(cat(S[i], "*", S[i+1])), string), S) = 0 then
return false
fi
od:
true
end proc:
select(filter, [$0..1000]); # Robert Israel, Oct 15 2014
MATHEMATICA
d[n_] := IntegerDigits[n]; Select[Range[0, 151], And @@ Table[MemberQ[FromDigits /@ Partition[d[#], IntegerLength[k], 1], k], {k, Times @@@ Partition[d[#], 2, 1]}] &] (* Jayanta Basu, Aug 10 2013 *)
PROG
(PARI) has(n, m)={ my(p=10^#Str(m)); until( m>n\=10, n%p==m & return(1))}
is_A203565(n)={ my(d); for(i=2, #d=eval(Vec(Str(n))), has(n, d[i]*d[i-1]) | return); 1 }
is_A203565(n)={ my(d=Vecsmall(Str(n))); for(i=2, #d, d[i]<50 & i++ & next; has(n, d[i-1]%48*(d[i]-48)) | return); 1 } /* twice as fast */
for( n=0, 999, is_A203565(n) & print1(n", "))
CROSSREFS
Cf. A203569 (digits are permutations of 0...n).
Cf. A227510 (product of all digits is a substring and > 0).
Sequence in context: A250395 A371123 A273880 * A132263 A089868 A089867
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 03 2012
STATUS
approved