A077715 - OEIS

%I #19 Jun 23 2022 15:42:12

%S 7,17,317,6317,26317,126317,2126317,72126317,372126317,5372126317,

%T 305372126317,9305372126317,409305372126317,20409305372126317,

%U 100020409305372126317,9100020409305372126317,209100020409305372126317,40209100020409305372126317

%N a(1) = 7; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.

%C a(n) is the smallest prime obtained by prefixing a(n-1) with a number of the form d*10^k where d is a single digit, 0 < d < 10, and k >= 0. Conjecture: d*10^k always exists.

%H Michael S. Branicky, <a href="/A077715/b077715.txt">Table of n, a(n) for n = 1..50</a>

%p a:= proc(n) option remember; local k, m, d, p;

%p       if n=1 then 7 else k:= a(n-1);

%p         for m from length(k) do

%p           for d to 9 do p:= k +d*10^m;

%p             if isprime(p) then return p fi

%p         od od

%p       fi

%p     end:

%p seq(a(n), n=1..20);  # _Alois P. Heinz_, Jan 12 2015

%o (Python)

%o from sympy import isprime

%o from itertools import islice

%o def agen(an=7):

%o     while True:

%o         yield an

%o         pow10 = 10**len(str(an))

%o         while True:

%o             found = False

%o             for t in range(pow10+an, 10*pow10+an, pow10):

%o                 if isprime(t):

%o                     an = t; found = True; break

%o             if found: break

%o             pow10 *= 10

%o print(list(islice(agen(), 18))) # _Michael S. Branicky_, Jun 23 2022

%Y Cf. A053584, A077713, A077714, A077716.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 19 2002

%E More terms from _Ray Chandler_, Jul 23 2003

%E Definition clarified by _N. J. A. Sloane_, Jan 19 2015