A120124 Smallest prime p such that p*10^n + 1 is a prime.

3, 7, 3, 7, 7, 61, 3, 7, 7, 3, 19, 37, 109, 79, 97, 13, 37, 19, 73, 103, 97, 283, 157, 61, 19, 61, 1213, 3, 163, 691, 367, 163, 181, 157, 241, 3, 103, 733, 151, 283, 337, 193, 211, 163, 7, 73, 307, 61, 223, 1549, 31, 127, 13, 547, 103, 151, 193, 811, 337, 19, 1021, 151

Offset

1,1

Comments

All terms belong to A007645. All terms also belong to A055664. Also many terms including the first 14 smallest primes from 3 to 139 {3,7,13,19,31,37,43,61,73,79,97,103,127,139} belong tpA023203. The smallest term that differs from A023203 is 151.

Links

Robert Israel, Table of n, a(n) for n = 1..1000 (first 300 terms from Vincenzo Librandi)

Example

a(1) = 3 because 31 = 3*10 + 1 is the smallest prime of form p*10 + 1, where p is a prime.
a(2) = 7 because 701 = 7*100 + 1 is the smallest prime of form p*100 + 1.

Maple

Primes:= select(isprime, [$1..10^5]):
for n from 1 to 1000 do
   for p in Primes do
      if isprime(p*10^n+1) then
        A[n]:= p
      fi
    od
od:
seq(A[n], n=1..1000); # Robert Israel, May 29 2014

Mathematica

prs=Prime[Range[2000]]; Table[i=1; While[!PrimeQ[First[Take[prs, {i}]] 10^n+1], i++]; Prime[i], {n, 200}] (* Harvey P. Dale, May 15 2011 *)

Crossrefs

Cf. A121172, A030430, A062800, A007645, A055664, A023203.

Sequence in context: A200481 A016665 A320831 * A151573 A113832 A115631

Adjacent sequences: A120121 A120122 A120123 * A120125 A120126 A120127

Keyword

nonn

Author

Alexander Adamchuk, Aug 15 2006

Status

approved