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A108537 Concatenation of palindrome k and its 10's complement is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A325476 A234536 A103737 * A219292 A181554 A116294

Adjacent sequences:  A108534 A108535 A108536 * A108538 A108539 A108540

KEYWORD

base,easy,nonn

AUTHOR

Jason Earls, Jul 25 2005

STATUS

approved

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Last modified June 22 11:59 EDT 2021. Contains 345375 sequences. (Running on oeis4.)