A108537 Concatenation of palindrome k and its 10's complement is prime.

1, 3, 7, 77, 99, 151, 161, 333, 707, 727, 737, 757, 949, 969, 989, 1441, 1551, 1771, 1881, 3003, 7227, 7667, 7997, 9009, 9339, 9999, 10001, 10101, 10701, 11111, 11611, 11711, 12221, 12921, 13231, 14341, 14841, 14941, 15851, 16661, 16961, 17071

Offset

1,2

Comments

Contains 10^k-1 for k in A056696, and (10^k-1)/9 for k in A108966. - Robert Israel, Jan 22 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(7)=161 because 1000-161 = 839 and 161839 is prime.

Maple

N:= 5: # for terms of <= N digits
digrev:= proc(n) local L, i;
   L:= convert(n, base, 10);
   add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
Res:= 1, 3, 7, 9:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Res:= Res, seq(seq((i*10^(m-1)+j)*10^m + digrev(i*10^(m-1)+j), j=0..10^(m-1)-1), i=[1, 3, 7, 9]);
  else
    m:= (d-1)/2;
    Res:= Res, seq(seq(seq((i*10^(m-1)+j)*10^(m+1)+y*10^m+digrev(i*10^(m-1)+j), y=0..9), j=0..10^(m-1)-1), i=[1, 3, 7, 9]);
  fi
od:
filter:= proc(t) local r;
  r:= 10^(ilog10(t)+1)-t;
  isprime(t*10^(ilog10(r)+1)+r)
end proc:
select(filter, [Res]); # Robert Israel, Jan 22 2019

Crossrefs

Cf. A056696, A108966.

Sequence in context: A234536 A103737 A354480 * A364660 A219292 A181554

Adjacent sequences: A108534 A108535 A108536 * A108538 A108539 A108540

Keyword

base,easy,nonn

Author

Jason Earls, Jul 25 2005

Status

approved