

A068395


a(n) = nth 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
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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 twodigit 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. 440442.


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 !! (n1)
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



