A308438 - OEIS

%I #23 Jun 01 2019 11:10:21

%S 11,223,31,401,547,619,773,8581,9109,10223,1129,12073,130553,14563,

%T 150011,161471,17257,18803,191189,20809,210557,225383,237091,240209,

%U 2509433,2613397,277429,283211,2901649,308153,313409,3204139,3300613,3419063,3507739,360091,3727313,3806347,3930061,4045421,41018911

%N a(n) is the smallest prime p whose decimal expansion begins with n and is such that the next prime is p+2n, or -1 if no such prime exists.

%H Chai Wah Wu, <a href="/A308438/b308438.txt">Table of n, a(n) for n = 1..100</a>

%e For n = 5, 547 is a prime starting with 5, and the next prime after 547 is 557 = 547 + 2*5.  Since this is the least number with these properties, a(5) = 547.

%p f:= proc(n) local d,p,q;

%p   for d from 0 do

%p     p:= nextprime(n*10^d-1);

%p     do

%p       q:= nextprime(p);

%p       if q - p = 2*n then return p fi;

%p       if q >= (n+1)*10^d then break fi;

%p       p:= q;

%p     od;

%p   od;

%p end proc:

%p map(f, [$1..50]);

%o (Python)

%o from sympy import nextprime

%o def A308438(n):

%o     l, p = 1, nextprime(n)

%o     while True:

%o         q = nextprime(p)

%o         if q-p == 2*n:

%o             return p

%o         p = q

%o         if p >= (n+1)*l:

%o             l *= 10

%o             p = nextprime(n*l) # _Chai Wah Wu_, May 31 2019

%Y Cf. A018800, A030665.

%K nonn,base,look

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, May 30 2019