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A113572
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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.
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2
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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; internal format)
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OFFSET
| 1,2
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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.
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LINKS
| Sean A. Irvine, Table of n, a(n) for n = 1..1000
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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.
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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 *)
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CROSSREFS
| Cf. A113573.
Sequence in context: A163574 A079847 A144165 * A037701 A037610 A035239
Adjacent sequences: A113569 A113570 A113571 * A113573 A113574 A113575
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KEYWORD
| base,easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 06 2005
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 29 2007
More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Jan 17 2011
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