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

Author

Reinhard Zumkeller, Mar 08 2002

Keywords

• nonn
• nice
• base

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

Examples

			a(10) = 29 - (2+9) = 18.
		

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.

Crossrefs

Cf. A065073.

Programs

Haskell

a068395 n = a068395_list !! (n-1)
a068395_list = zipWith (-) a000040_list a007605_list
-- Reinhard Zumkeller, Aug 04 2011

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 *)

Formula

a(n) = A000040(n) - A007953(A000040(n)).

Extensions

More terms from Stefan Steinerberger, Apr 01 2006