The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A203565 Numbers that contain the product of any two adjacent digits as a substring. 9
 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 (list; graph; refs; listen; history; text; internal format)
 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 Jayanta Basu, Table of n, a(n) for n = 1..1000 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. also A203566, A198298, A236402, A236403, A236404. Cf. A227510 (product of all digits is a substring and > 0). Sequence in context: A108192 A250395 A273880 * A132263 A089868 A089867 Adjacent sequences:  A203562 A203563 A203564 * A203566 A203567 A203568 KEYWORD nonn,base AUTHOR M. F. Hasler, Jan 03 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 18 17:51 EDT 2021. Contains 345120 sequences. (Running on oeis4.)