A121066 Least positive k such that 10^n + {k, k+2, k+6, k+8} are all prime.

4, 1, 1, 481, 3001, 1111, 2341, 13951, 5461, 25261, 57421, 7531, 123691, 56581, 945721, 67441, 1346491, 325231, 430711, 2139271, 2561161, 81721, 4319041, 571381, 4331251, 1232251, 7114471, 3185011, 407581, 1500631, 1846021, 1346611

Offset

0,1

Comments

For n >= 1, k == 1 (mod 30). - Robert Israel, May 06 2015

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 0..105

Maple

A[0]:= 4:
for n from 1 to 30 do
  for k from 1 by 30 do
     if andmap(isprime, map(`+`, [0, 2, 6, 8], 10^n+k)) then
        A[n]:= k; break
     fi;
od od:
seq(A[n], n=0..30); # Robert Israel, May 06 2015

Mathematica

lpk[n_]:=Module[{k=1, x=10^n}, While[AnyTrue[x+ k+{0, 2, 6, 8}, CompositeQ], k++]; k]; Table[lpk[n], {n, 0, 15}] (* The program generates the first 16 terms of the sequence. *) (* Harvey P. Dale, Jun 18 2022 *)

Prog

(PARI) print1(4, ", "); n=0; until(n==100, n++; x=1; y=0; until(y==1, if(isprime(10^n+x), if(isprime(10^n+x+2), if(isprime(10^n+x+6), if(isprime(10^n+x+8), y++, x=x+30), x=x+30), x=x+30), x=x+30); if(y==1, print1(x, ", ")))) \\ Tim Johannes Ohrtmann, May 04 2015
(PARI) a(n)=if(n==0, return(4)); my(k=10^n+1); while(!isprime(k) || !isprime(k+2) || !isprime(k+6) || !isprime(k+8), k+=30); k-10^n \\ Charles R Greathouse IV, May 06 2015

Crossrefs

Cf. A064281.

Sequence in context: A102602 A156951 A357052 * A343635 A287647 A331749

Adjacent sequences: A121063 A121064 A121065 * A121067 A121068 A121069

Keyword

nonn

Author

Jason Earls, Aug 10 2006

Status

approved