OFFSET
1,2
COMMENTS
a(5*t)=0, for all t>1. This is because the last digit of 5*t is always 0 or 5 yet we require this digit to be composite for t>1. There are no other zero terms below a(10000). Conjecture: No other term is zero.
Because 0 is neither prime nor composite, it does not appear in any nonzero term. The digit 1 may appear only as the first digit of a term.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..1000
EXAMPLE
a(6) = 122424, the first digit is 1, the 2nd, 3rd and the 5th digits are primes and the 4th and 6th digit are composite.
MATHEMATICA
okQ[n_]:=Module[{d=IntegerDigits[n], ok, i=1}, ok=(d[[1]]==1); While[i<Length[d]&&ok, i++; ok=If[PrimeQ[i], MemberQ[{2, 3, 5, 7}, d[[i]]], MemberQ[{4, 6, 8, 9}, d[[i]]]]]; ok]; Table[mn=Ceiling[10^(n-1)/n]; mx=Floor[(10^n-1)/n]; i=mn; While[i<mx&&!okQ[i*n], i++]; If[i<=mx, i*n, 0], {n, 8}] (* slow *)
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Amarnath Murthy, Nov 06 2005
EXTENSIONS
Corrected and extended by R. J. Mathar, Aug 29 2007
More terms from Sean A. Irvine, Jan 17 2011
STATUS
approved