A258337 Smallest prime starting with n that does not appear earlier.

11, 2, 3, 41, 5, 61, 7, 83, 97, 101, 113, 127, 13, 149, 151, 163, 17, 181, 19, 2003, 211, 223, 23, 241, 251, 263, 271, 281, 29, 307, 31, 3203, 331, 347, 353, 367, 37, 383, 397, 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

Offset: 1

Author

Vladimir Shevelev, May 27 2015

Keywords

• nonn
• base

Comments

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.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5000
• Index entries for primes involving decimal expansion of n

Crossrefs

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

Programs

Haskell

import Data.List (isPrefixOf, delete)
a258337 n = a258337_list !! (n-1)
a258337_list = f 1 $ map show a000040_list where
   f x pss = g pss where
     g (qs:qss) = if show x `isPrefixOf` qs
                     then (read qs :: Int) : f (x + 1) (delete qs pss)
                     else g qss
-- Reinhard Zumkeller, Jul 01 2015

Maple

N:= 100: # to get a(1) to a(N)
for n from 1 to N do
  p:= n;
  if n < 10 then
    p1:= 0
  else
    p1:= A[floor(n/10)];
  fi;
  if isprime(p) and p > p1 then
     A[n]:= p
  else
    for d from 1 while not assigned(A[n]) do
      for i from 1 to 10^d-1 do
        p:= 10^d*n+i;
        if p > p1 and isprime(p) then
           A[n]:= p;
           break
        fi;
      od
    od
  fi
od:
seq(A[i],i=1..N); # Robert Israel, Jun 29 2015

PARI

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

Formula

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

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