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A068811
Numbers k such that k and its 10's complement (10^d-k, where d is the number of digits in k) are both primes
11
3, 5, 7, 11, 17, 29, 41, 47, 53, 59, 71, 83, 89, 97, 113, 137, 173, 179, 191, 227, 239, 257, 281, 317, 347, 353, 359, 383, 401, 431, 443, 479, 491, 509, 521, 557, 569, 599, 617, 641, 647, 653, 683, 719, 743, 761, 773, 809, 821, 827, 863, 887, 911, 929, 941
OFFSET
1,1
COMMENTS
In other words, primes p such that the difference between the smallest power of 10 exceeding p and p is prime. - Zak Seidov, Feb 27 2004
a(n) = 10^d - A145985(n), where d is the number of digits in A145985(n). - N. J. A. Sloane, Dec 18 2022
The only twin prime pairs in the sequence are (3,5) and (5,7). This is easily seen by mod 6 congruences using 10^k = 4 (mod 6). - Giuseppe Coppoletta, Jul 24 2016
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 1000 terms from Vincenzo Librandi]
EXAMPLE
47 is a prime; the smallest power of 10 exceeding 47 is 100 and 100 - 47 = 53 is prime. Therefore 47 is in the sequence.
641 is a term as 641 and 1000-641 = 359 are primes.
MAPLE
a:=[];
for i from 1 to 1000 do
p:=ithprime(i); d:=length(p); q:=10^d-p;
if isprime(q) then a:=[op(a), p]; fi; od:
a; # N. J. A. Sloane, Dec 18 2022
MATHEMATICA
Select[Prime[Range[160]], PrimeQ[10^(Floor[Log[10, # ]] + 1) - # ] &] (* Stefan Steinerberger, Jun 15 2007 *)
PROG
(PARI) is_A068811(p)= isprime(10^#Str(p)-p) & isprime(p) \\ M. F. Hasler, May 01 2012
(PARI) for(d=1, 4, forprime(p=10^(d-1), 10^d, if(isprime(10^d-p), print1(p", ")))) \\ Charles R Greathouse IV, May 01 2012
(Sage) [p for p in prime_range(100) if is_prime(10^p.ndigits()-p)] # Giuseppe Coppoletta, Jul 24 2016
CROSSREFS
Cf. A145985.
Sequence in context: A241896 A076186 A092564 * A145987 A088083 A116457
KEYWORD
easy,nonn,base
AUTHOR
Amarnath Murthy, Mar 07 2002
EXTENSIONS
Corrected by Jason Earls, May 25 2002
Edited by N. J. A. Sloane, Sep 18 2008 at the suggestion of R. J. Mathar
STATUS
approved