A145985 Primes resulting from subtracting primes from 10^n in order (see Comments for precise definition).

7, 5, 3, 89, 83, 71, 59, 53, 47, 41, 29, 17, 11, 3, 887, 863, 827, 821, 809, 773, 761, 743, 719, 683, 653, 647, 641, 617, 599, 569, 557, 521, 509, 491, 479, 443, 431, 401, 383, 359, 353, 347, 317, 281, 257, 239, 227, 191, 179, 173, 137, 113, 89, 71, 59, 53, 47, 29, 23, 17, 3, 8969, 8951, 8849, 8837, 8819, 8807, 8783

Offset: 1

Author

Enoch Haga, Oct 27 2008

Keywords

• easy
• nonn

Comments

Comments from N. J. A. Sloane, Dec 18 2022 (Start)

A more precise definition is the following.

Start with k=1; let N=10^k, let i run from 10^(k-1)-1 to N-1, let j = N-i, if i and j are both primes, append j to the sequence; increment k.

This is derived from A068811 via a(n) = 10^d - A068811(n) where d is the number of digits in A068811(n). A068811 is more fundamental, for there the primes appear in order and there are no duplicates. (End)

Primes may appear more than once.

Examples

			887 is a term because 1000-887 = 113 and both 887 and 113 are prime.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 1000 terms from _Harvey P. Dale_]
• N. J. A. Sloane, Table of n, a(n) for n = 1..80338

Crossrefs

Cf. A068811, A358310, A359121, A359122, A359123.

See A359120 for the length of the n-th block of decreasing terms.

Programs

Maple

a:=[];
for k from 1 to 6 do
N := 10^k;
   for i from 10^(k-1)+1 to N-1 do
      j:=N-i;
      if isprime(i) and isprime(j) then a:=[op(a),j]; fi;
   od:
od;
a; # N. J. A. Sloane, Dec 16 2022

Mathematica

Select[Table[10^IntegerLength[p]-p,{p,Prime[Range[200]]}],PrimeQ] (* Harvey P. Dale, Dec 16 2022 *)

Extensions

Corrected and edited by Harvey P. Dale and N. J. A. Sloane, Dec 16 2022