A158025 Sides of squares which are filled exactly (no holes, no overlaps) by the digits needed to write a subsequence of consecutive Primes starting with 2.

1, 2, 4, 6, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 72, 73, 77, 78, 82, 83, 87, 88, 92, 93, 97, 98, 102, 103, 107, 108, 112, 113, 117, 118, 122, 123, 127, 128, 132, 133, 137, 138, 142, 143, 147, 148, 152, 153, 157, 158, 162, 163, 167, 168, 172, 173, 177, 178, 182, 183

Offset

1,2

Comments

The primes fitting exactly in a "Primes-digits square" are given by A158024. Terms computed by Jean-Marc Falcoz.

Links

Robert Israel, Table of n, a(n) for n = 1..3000

Eric Angelini, Digit Spiral

E. Angelini, Digit Spiral [Cached copy, with permission]

Example

...2...23...2357
.......57...1113
............1719
............2329
The above squares, filled exactly by a subsequence of consecutive primes starting with 2 have sides 1, 2, 4. There is no side-3 square with this property. The next properly filled square will have side 6.

Maple

X:= 0: p:= 1:
Res:= NULL: count:= 0:
while count < 100 do
  p:= nextprime(p);
  X:= X + ilog10(p) + 1;
  if issqr(X) then Res:= Res, sqrt(X); count:= count+1: fi
od:
Res; # Robert Israel, Jan 13 2020

Crossrefs

Sequence in context: A121538 A339508 A275844 * A216345 A026510 A138204

Adjacent sequences: A158022 A158023 A158024 * A158026 A158027 A158028

Keyword

base,nonn

Author

Eric Angelini, Mar 11 2009

Status

approved