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

1, 2, 5, 6, 9, 10, 10, 15, 15, 16, 18, 24, 18, 26, 24, 30, 27, 33, 28, 40, 33, 40, 35, 48, 37, 50, 42, 53, 45, 58, 46, 64, 50, 64, 54, 72, 55, 73, 60, 78, 63, 82, 63, 88, 69, 88, 72, 95, 73, 98, 78, 102, 80, 106, 82, 112, 87, 111, 90, 120, 91, 122, 95, 126, 99, 130, 100, 135

Offset: 3

Author

Simon Plouffe, N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn
• base

Examples

			a(3) = 1: The only base number of length 2*3 + 1 = 7 is 1109111 = A060087(1);
a(4) = 2 indicates the existence of two length 2*4 + 1 = 9 base numbers, 110091011 = A060087(2) and 111091111 = A060087(3).
		

References

• M. Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124-132.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Hugo Pfoertner, Table of n, a(n) for n = 3..115
• Patrick De Geest, Subsets of Palindromic Squares
• IBM Research Ponder This, Non-palindromic numbers with palindromic squares, October 2023 - Challenge.
• M. Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124-132. [Annotated scanned copy]. See foot of page 130.
• G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Crossrefs

Cf. A002778, A002779, A060087, A060088.

Programs

PARI

\\ see P. De Geest link.

Extensions

a(17)-a(31) from Sean A. Irvine, Jan 10 2018

Name and offset corrected by Hugo Pfoertner, Oct 04 2023

a(32)-a(70) from Hugo Pfoertner, Oct 07 2023