OFFSET
1,2
COMMENTS
All numbers with at least one zero digit have a product of digits which is a substring; these have been kept out by the restriction on positivity.
The sequence is infinite: if n is a term 10n+1 is also a term. Are there any other patterns (except for prepending 1 to any term)? - Zak Seidov, Jul 24 2013
You can also insert 1 in any position outside the substring that gives the product of digits. - Robert Israel, Aug 26 2014
See also A203566 for a nontrivial subsequence of A203565. The zeroless members of the latter differ from this sequence from 212 on which is there but not here, while 236 is the first here but not there. - M. F. Hasler, Oct 14 2014
LINKS
Zak Seidov, Table of n, a(n) for n = 1..10000
EXAMPLE
The product of the digits of 236 is 36, a substring of 236, and hence 236 is a member.
MAPLE
filter:= proc(n)
local L;
L:= convert(n, base, 10);
if has(L, 0) then return false fi;
verify(convert(convert(L, `*`), base, 10), L, 'sublist');
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 26 2014
MATHEMATICA
Select[Range[650], FreeQ[x = IntegerDigits[#], 0] && MemberQ[FromDigits /@ Partition[x, IntegerLength[y = Times @@ x], 1], y] &]
PROG
(Python)
from operator import mul
from functools import reduce
A227510 = [int(n) for n in (str(x) for x in range(1, 10**5)) if
..........not n.count('0') and str(reduce(mul, (int(d) for d in n))) in n]
# Chai Wah Wu, Aug 26 2014
(PARI) {isok(n)=d=digits(n); p=prod(i=1, #d, d[i]); k=1; while(p&&k<=(#d-#digits(p)+1), v=[]; for(j=k, k+#digits(p)-1, v=concat(v, d[j])); if(v==digits(p), return(1)); k++); return(0); }
n=1; while(n<10^4, if(isok(n), print1(n, ", ")); n++) \\ Derek Orr, Aug 26 2014
(PARI) is_A227510(n)={(t=digits(prod(i=1, #n=digits(n), n[i])))&&for(i=0, #n-#t, vecextract(n, 2^(i+#t)-2^i)==t&&return(1))} \\ M. F. Hasler, Oct 14 2014
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jayanta Basu, Jul 14 2013
EXTENSIONS
Edited by M. F. Hasler, Oct 14 2014
STATUS
approved