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%I #22 Aug 26 2015 01:51:04
%S 0,0,0,0,9,9,9,9,18,18,27,27,36,36,36,45,45,54,54,63,63,63,72,72,81,
%T 99,99,99,99,108,117,126,126,126,135,144,144,153,153,162,162,171,180,
%U 180,180,180,207,216,216,216,225,225,234,243,243,252,252,261,261,270
%N a(n) = n-th prime minus its sum of digits.
%C a(i) <= a(j) for i < j.
%C A number and the sum of its digits have the same value modulo 9. Hence all terms are divisible by 9. - _Stefan Steinerberger_, Apr 01 2006
%C A192977 gives number of occurrences of multiples of 9. - _Reinhard Zumkeller_, Aug 04 2011
%C Margaret Coffey (ed.) p. 440: "The sum of the digits of a two-digit prime number is subtracted from the number. Prove that the difference cannot be a prime number." Proof [p.442] "Let a and b be the tens and units digits, respectively, and let 10a+b be the prime. Subtract the sum of the digits from the number: 10a + b - (a+b) = 9a. The difference is a multiple of 9 and cannot, therefore, be prime." - _Jonathan Vos Post_, Feb 02 2012
%H Reinhard Zumkeller, <a href="/A068395/b068395.txt">Table of n, a(n) for n = 1..10000</a>
%H Margaret Coffey, Editor, <a href="http://www.jstor.org/stable/10.5951/mathteacher.105.6.0440">Problem #3, Calendar</a>, Mathematics Teacher, March 2012, pp. 440-442.
%F a(n) = A000040(n) - A007953(A000040(n)).
%e a(10) = 29 - (2+9) = 18.
%t Table[Prime[n] - Sum[DigitCount[Prime[n]][[i]]*i, {i, 1, 9}], {n, 1, 60}] (* _Stefan Steinerberger_, Apr 01 2006 *)
%t #-Total[IntegerDigits[#]]&/@Prime[Range[60]] (* _Harvey P. Dale_, Oct 14 2014 *)
%o (Haskell)
%o a068395 n = a068395_list !! (n-1)
%o a068395_list = zipWith (-) a000040_list a007605_list
%o -- _Reinhard Zumkeller_, Aug 04 2011
%Y Cf. A065073.
%K nonn,nice,base
%O 1,5
%A _Reinhard Zumkeller_, Mar 08 2002
%E More terms from _Stefan Steinerberger_, Apr 01 2006
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