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A007573 a(n) is the number of base numbers with 2n+1 digits in the asymmetric families of palindromic squares.

%I A007573 M1319 #29 Nov 04 2023 14:01:02
%S A007573 1,2,5,6,9,10,10,15,15,16,18,24,18,26,24,30,27,33,28,40,33,40,35,48,
%T A007573 37,50,42,53,45,58,46,64,50,64,54,72,55,73,60,78,63,82,63,88,69,88,72,
%U A007573 95,73,98,78,102,80,106,82,112,87,111,90,120,91,122,95,126,99,130,100,135
%N A007573 a(n) is the number of base numbers with 2n+1 digits in the asymmetric families of palindromic squares.
%D A007573 M. Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124-132.
%D A007573 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007573 Hugo Pfoertner, <a href="/A007573/b007573.txt">Table of n, a(n) for n = 3..115</a>
%H A007573 Patrick De Geest, <a href="http://www.worldofnumbers.com/subsquar.htm#Squarcore">Subsets of Palindromic Squares</a>
%H A007573 IBM Research Ponder This, <a href="https://research.ibm.com/haifa/ponderthis/challenges/October2023.html">Non-palindromic numbers with palindromic squares</a>, October 2023 - Challenge.
%H A007573 M. Keith, <a href="/A002778/a002778_1.pdf">Classification and enumeration of palindromic squares</a>, J. Rec. Math., 22 (No. 2, 1990), 124-132. [Annotated scanned copy]. See foot of page 130.
%H A007573 G. J. Simmons, <a href="/A002778/a002778.pdf">On palindromic squares of non-palindromic numbers</a>, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]
%e A007573 a(3) = 1: The only base number of length 2*3 + 1 = 7 is 1109111 = A060087(1);
%e A007573 a(4) = 2 indicates the existence of two length 2*4 + 1 = 9 base numbers, 110091011 = A060087(2) and 111091111 = A060087(3).
%o A007573 (PARI) \\ see P. De Geest link.
%Y A007573 Cf. A002778, A002779, A060087, A060088.
%K A007573 nonn,base
%O A007573 3,2
%A A007573 _Simon Plouffe_, _N. J. A. Sloane_, _Robert G. Wilson v_
%E A007573 a(17)-a(31) from _Sean A. Irvine_, Jan 10 2018
%E A007573 Name and offset corrected by _Hugo Pfoertner_, Oct 04 2023
%E A007573 a(32)-a(70) from _Hugo Pfoertner_, Oct 07 2023