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A113572 Least n-digit multiple of n such that the r-th digit is prime if r is a prime else it is composite. The location and value of the most significant digit is 1. 0 if no such number exists. 2
1, 12, 123, 1224, 12245, 122424, 1224265, 12242424, 122424246, 0, 12242424447, 122424244428, 1224242444243, 12242424442458, 0, 1224242444242448, 12242424442424692, 122424244424244828, 1224242444242444367, 0 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A113573.
Sequence in context: A278983 A079847 A144165 * A037701 A037610 A035239
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

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)