OFFSET
1,1
COMMENTS
This means: by removing any (possibly none) of the decimal digits of any member of A002144 one can obtain some number of this sequence here.
The basic algorithm is: if no substring of p matches any previously found prime, add p to the list.
The basic theorem of minimal sets says that the minimal set is always finite.
LINKS
Walter A. Kehowski and Curtis Bright, Table of n, a(n) for n = 1..146 (first 135 terms from Walter A. Kehowski)
C. Rivera, Shallit Minimal Primes Set (Puzzle No. 178), PrimePuzzle.net.
J. Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.
EXAMPLE
a(11)=101 since the pattern "*1*0*1*" does not occur in any previously found prime of the form 4n+1. Assuming all previous members of the list have been similarly recursively constructed, then 109 is the next prime in the list.
MAPLE
with(StringTools);
wc := proc(s) cat("*", Join(convert(s, list), "*"), "*") end;
M1:=[]: wcM1:=[]: p:=1: for z from 1 to 1 do for k while p<10^11 do p:=nextprime(p);
if k mod 100000 = 0 then print(k, p, evalf((time()-st)/60, 4)) fi;
if p mod 4 = 1 then sp:=convert(p, string); if andmap(proc(w) not(WildcardMatch(w, sp)) end, wcM1) then
M1:=[op(M1), p]; wcM1:=[op(wcM1), wc(sp)]; print(p) fi fi od od;
CROSSREFS
KEYWORD
base,fini,nonn,full
AUTHOR
Walter Kehowski, Oct 06 2005
EXTENSIONS
Shortened definition; moved some material from the examples to the comments - R. J. Mathar, May 24 2010
STATUS
approved