A092245 Lesser of the first twin prime pair with n digits.

3, 11, 101, 1019, 10007, 100151, 1000037, 10000139, 100000037, 1000000007, 10000000277, 100000000817, 1000000000061, 10000000001267, 100000000000097, 1000000000002371, 10000000000001549, 100000000000000019

Offset

1,1

Comments

Sum of reciprocals = 0.43523579465477...

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000 First 101 from Abhiram R Devesh

Formula

a(n) = A124001(n-1) + 10^(n-1). - Robert G. Wilson v, Nov 28 2015

Maple

for n from 1 to 100 do
  r:= 10^(n-1);
  p:= nextprime(r); q:= nextprime(p);
  while q - p > 2 do
    p:= q; q:= nextprime(p);
  od;
  A[n]:= p;
od:
seq(A[n], n=1..100); # Robert Israel, Aug 04 2014

Mathematica

a[n_] := Block[{p = NextPrime[10^(n -1)]}, While[ !PrimeQ[p +2], p = NextPrime@ p]; p]; Array[a, 18] (* Robert G. Wilson v, Dec 04 2022 *)

Prog

(PARI) firsttwpr(n) = { sr=0; for(m=0, n, c=0; for(x=10^m+1, 10^(m+1), if(isprime(x)&& isprime(x+2), print1(x", "); sr+=1./x; break) ) ); print(); print(sr) }
(Python)
import sympy
for i in range(100):
    p=sympy.nextprime(10**i)
    while not sympy.isprime(p+2):
        p=sympy.nextprime(p)
    print(p)
# Abhiram R Devesh, Aug 02 2014

Crossrefs

Cf. A092250, A124001.

Sequence in context: A154299 A007616 A121045 * A238446 A337734 A302927

Adjacent sequences: A092242 A092243 A092244 * A092246 A092247 A092248

Keyword

base,nonn

Author

Cino Hilliard, Feb 17 2004

Extensions

Corrected by T. D. Noe, Nov 15 2006

Status

approved