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

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

Adjacent sequences: A068808 A068809 A068810 * A068812 A068813 A068814

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