A068395 a(n) = n-th prime minus its sum of digits.

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

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