cp's OEIS Frontend

A158024 Primes p such that all the digits needed to write the consecutive Primes from 2 to p fill exactly a square (no holes, no overlaps).

%I A158024 #9 Jan 13 2020 20:41:53
%S A158024 2,7,29,71,101,127,191,229,317,379,499,577,733,823,10867,11159,12301,
%T A158024 12577,13781,14107,15391,15733,17183,17509,19079,19457,21023,21467,
%U A158024 23059,23549,25339,25793,27733,28151,30161,30697,32719,33247,35401
%N A158024 Primes p such that all the digits needed to write the consecutive Primes from 2 to p fill exactly a square (no holes, no overlaps).
%C A158024 The sides of the successive squares are given by A158025. Terms computed by _Jean-Marc Falcoz_.
%H A158024 Robert Israel, <a href="/A158024/b158024.txt">Table of n, a(n) for n = 1..3000</a>
%H A158024 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DigitSpiral.htm">Digit Spiral</a>
%H A158024 E. Angelini, <a href="/A158022/a158022.pdf">Digit Spiral</a> [Cached copy, with permission]
%e A158024 ...2...23...2357
%e A158024 .......57...1113
%e A158024 ............1719
%e A158024 ............2329
%e A158024 The primes fitting exactly in the SE corner of the above squares are 2, 7, 29. There is no 3X3 square where this is possible.
%p A158024 X:= 0: p:= 1:
%p A158024 Res:= NULL: count:= 0:
%p A158024 while count < 100 do
%p A158024   p:= nextprime(p);
%p A158024   X:= X + ilog10(p) + 1;
%p A158024   if issqr(X) then Res:= Res,p; count:= count+1 fi
%p A158024 od:
%p A158024 Res; # _Robert Israel_, Jan 13 2020
%K A158024 base,nonn
%O A158024 1,1
%A A158024 _Eric Angelini_, Mar 11 2009