A258337 - OEIS

%I #32 Nov 11 2020 19:05:36

%S 11,2,3,41,5,61,7,83,97,101,113,127,13,149,151,163,17,181,19,2003,211,

%T 223,23,241,251,263,271,281,29,307,31,3203,331,347,353,367,37,383,397,

%U 401,419,421,43,443,457,461,47,487,491,503,5101,521,53,541,557,563,571,587,59,601,613,6203,631,641,653,661,67,683,691,701

%N Smallest prime starting with n that does not appear earlier.

%C According to a comment in A018800, every term exists. So the sequence is a permutation of the primes. Indeed, every prime p appears in the sequence either as the p-th term or earlier.

%H Peter J. C. Moses, <a href="/A258337/b258337.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>

%F For n>=2, a(n) >= prime(n-1). The equality holds iff prime(n-1) did not already appear as a(k), k<n.

%p N:= 100: # to get a(1) to a(N)

%p for n from 1 to N do

%p   p:= n;

%p   if n < 10 then

%p     p1:= 0

%p   else

%p     p1:= A[floor(n/10)];

%p   fi;

%p   if isprime(p) and p > p1 then

%p      A[n]:= p

%p   else

%p     for d from 1 while not assigned(A[n]) do

%p       for i from 1 to 10^d-1 do

%p         p:= 10^d*n+i;

%p         if p > p1 and isprime(p) then

%p            A[n]:= p;

%p            break

%p         fi;

%p       od

%p     od

%p   fi

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Jun 29 2015

%o (PARI) sw(m,n)=d1=digits(n);d2=digits(m);for(i=1,min(#d1,#d2),if(d1[i]!=d2[i],return(0)));1

%o v=[];n=1;while(n<70,k=1;while(k<10^3,p=prime(k);if(sw(p,n)&&!vecsearch(vecsort(v),p),v=concat(v,p);k=0;n++);k++));v \\ _Derek Orr_, Jun 13 2015

%o (Haskell)

%o import Data.List (isPrefixOf, delete)

%o a258337 n = a258337_list !! (n-1)

%o a258337_list = f 1 $ map show a000040_list where

%o    f x pss = g pss where

%o      g (qs:qss) = if show x `isPrefixOf` qs

%o                      then (read qs :: Int) : f (x + 1) (delete qs pss)

%o                      else g qss

%o -- _Reinhard Zumkeller_, Jul 01 2015

%Y Cf. A000040, A018800, A030665, A062584, A258190, A258339.

%K nonn,base

%O 1,1

%A _Vladimir Shevelev_, May 27 2015