A007573 a(n) is the number of base numbers with 2n+1 digits in the asymmetric families of palindromic squares. (Formerly M1319)

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

3,2

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]

Example

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).

Prog

(PARI) \\ see P. De Geest link.

Crossrefs

Cf. A002778, A002779, A060087, A060088.

Sequence in context: A269472 A351830 A244272 * A285663 A143909 A284507

Adjacent sequences: A007570 A007571 A007572 * A007574 A007575 A007576

Keyword

nonn,base

Author

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

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

Status

approved