A095188 Smallest prime formed by the digit string after decimal point of n^(1/2), or 0 if no such prime exists.

0, 41, 7, 0, 2, 449, 645751, 82842712474619, 0, 162277, 3, 464101615137754587054892683011, 605551, 7, 87298334620741688517926539978239961, 0, 1231, 2, 3, 47, 5

Offset

1,2

Comments

Conjecture: a(n) is nonzero if n is not a perfect square.

For n=22, no provable primes were found with fewer than 256 digits. - Wouter Meeussen, Jun 04 2004

Links

Table of n, a(n) for n=1..21.

Example

a(7) = 645751 as 7^(1/2) = 2.64575131106459059... and the least prime is 645751.

Mathematica

<< NumberTheory`PrimeQ`; it = Table[{n, k = 1; While[temp = Floor[10^k FractionalPart[n^(1/2)]]; k < 256 && (temp === 1 || ! ProvablePrimeQ[temp]), k++ ]; temp, k}, {n, 2, 21}]

Crossrefs

Sequence in context: A198190 A106424 A126636 * A215540 A107813 A198162

Adjacent sequences: A095185 A095186 A095187 * A095189 A095190 A095191

Keyword

base,nonn

Author

Amarnath Murthy, Jun 02 2004

Extensions

Corrected and extended by Wouter Meeussen, Jun 04 2004

Status

approved