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A111055 The set of primes of the form 4n+1 that is minimal in the sense of A071062. 6
5, 13, 17, 29, 37, 41, 61, 73, 89, 97, 101, 109, 149, 181, 233, 277, 281, 349, 409, 433, 449, 677, 701, 709, 769, 821, 877, 881, 1669, 2221, 3001, 3121, 3169, 3221, 3301, 3833, 4969, 4993, 6469, 6833, 6949, 7121, 7477, 7949, 9001, 9049, 9221, 9649, 9833 (list; graph; refs; listen; history; text; internal format)
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

Cf. A071062, A071070, A110600, A110615.

Sequence in context: A280084 A319287 A192592 * A307096 A283391 A145016

Adjacent sequences:  A111052 A111053 A111054 * A111056 A111057 A111058

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

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)