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 A068395 a(n) = n-th prime minus its sum of digits. 7
 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, 99, 99, 99, 99, 108, 117, 126, 126, 126, 135, 144, 144, 153, 153, 162, 162, 171, 180, 180, 180, 180, 207, 216, 216, 216, 225, 225, 234, 243, 243, 252, 252, 261, 261, 270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(i) <= a(j) for i < j. 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 A192977 gives number of occurrences of multiples of 9. - Reinhard Zumkeller, Aug 04 2011 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 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Margaret Coffey, Editor, Problem #3, Calendar, Mathematics Teacher, March 2012, pp. 440-442. FORMULA a(n) = A000040(n) - A007953(A000040(n)). EXAMPLE a(10) = 29 - (2+9) = 18. MATHEMATICA Table[Prime[n] - Sum[DigitCount[Prime[n]][[i]]*i, {i, 1, 9}], {n, 1, 60}] (* Stefan Steinerberger, Apr 01 2006 *) #-Total[IntegerDigits[#]]&/@Prime[Range[60]] (* Harvey P. Dale, Oct 14 2014 *) PROG (Haskell) a068395 n = a068395_list !! (n-1) a068395_list = zipWith (-) a000040_list a007605_list -- Reinhard Zumkeller, Aug 04 2011 CROSSREFS Cf. A065073. Sequence in context: A216852 A251558 A251559 * A245429 A242893 A275485 Adjacent sequences: A068392 A068393 A068394 * A068396 A068397 A068398 KEYWORD nonn,nice,base AUTHOR Reinhard Zumkeller, Mar 08 2002 EXTENSIONS More terms from Stefan Steinerberger, Apr 01 2006 STATUS approved

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Last modified February 24 14:16 EST 2024. Contains 370304 sequences. (Running on oeis4.)