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A111056 Minimal set of prime-strings in base 10 for primes of the form 4n+3 in the sense of A071062. 1
3, 7, 11, 19, 59, 251, 491, 499, 691, 991, 2099, 2699, 2999, 4051, 4451, 4651, 5051, 5651, 5851, 6299, 6451, 6551, 6899, 8291, 8699, 8951, 8999, 9551, 9851, 22091, 22291, 66851, 80051, 80651, 84551, 85451, 86851, 88651, 92899, 98299, 98899 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The basic rule is: if no substring of p matches any smaller prime of the form 4n+3, add p to the list. The basic theorem of minimal sets says that the minimal set is always finite.

The sequence b-file is complete except for the number (2*10^19153 + 691)/9, i.e., the decimal number consisting of 19151 "2"s followed by two "9"s. - Curtis Bright, Jan 23 2015

LINKS

Walter A. Kehowski and Curtis Bright, Table of n, a(n) for n = 1..112 (first 103 terms from Walter A. Kehowski)

Walter A. Kehowski, Full list of terms

C. Rivera, Shallit Minimal Primes Set (Puzzle No. 178), PrimePuzzle.net.

F. Morain, Primality certificate for the largest number of A111056, May 4 2015

J. Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.

EXAMPLE

From Danny Rorabaugh, Mar 26 2015: (Start)

a(5) is not 23, even though 23 is the fifth prime of the form 4n+3, since 23 contains a(1)=3 as a substring. Similarly: 31 and 43 contain 3 and 47 contains a(2)=7. Thus a(5)=59.

This sequence contains 2099 since 2, 0, 9, 20, 09, 99, 209, 299, and 099 are not primes of the form 4n+3.

(End)

MAPLE

with(StringTools); wc := proc(s) cat("*", Join(convert(s, list), "*"), "*") end; M3:=[]: wcM3:=[]: 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 = 3 then sp:=convert(p, string); if andmap(proc(w) not(WildcardMatch(w, sp)) end, wcM3) then M3:=[op(M3), p]; wcM3:=[op(wcM3), wc(sp)]; print(p) fi fi od od; # Let it run for a couple of days.

CROSSREFS

Cf. A071062, A071070, A110600, A110615.

Sequence in context: A191245 A282914 A284027 * A083908 A050577 A283178

Adjacent sequences:  A111053 A111054 A111055 * A111057 A111058 A111059

KEYWORD

base,fini,nonn,uned

AUTHOR

Walter Kehowski, Oct 06 2005

STATUS

approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)