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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.

%I A158025 #9 Jan 13 2020 20:42:01
%S A158025 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,
%T A158025 98,102,103,107,108,112,113,117,118,122,123,127,128,132,133,137,138,
%U A158025 142,143,147,148,152,153,157,158,162,163,167,168,172,173,177,178,182,183
%N 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.
%C A158025 The primes fitting exactly in a "Primes-digits square" are given by A158024. Terms computed by _Jean-Marc Falcoz_.
%H A158025 Robert Israel, <a href="/A158025/b158025.txt">Table of n, a(n) for n = 1..3000</a>
%H A158025 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DigitSpiral.htm">Digit Spiral</a>
%H A158025 E. Angelini, <a href="/A158022/a158022.pdf">Digit Spiral</a> [Cached copy, with permission]
%e A158025 ...2...23...2357
%e A158025 .......57...1113
%e A158025 ............1719
%e A158025 ............2329
%e A158025 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.
%p A158025 X:= 0: p:= 1:
%p A158025 Res:= NULL: count:= 0:
%p A158025 while count < 100 do
%p A158025   p:= nextprime(p);
%p A158025   X:= X + ilog10(p) + 1;
%p A158025   if issqr(X) then Res:= Res,sqrt(X); count:= count+1: fi
%p A158025 od:
%p A158025 Res; # _Robert Israel_, Jan 13 2020
%K A158025 base,nonn
%O A158025 1,2
%A A158025 _Eric Angelini_, Mar 11 2009