[math-fun] 73 (was Re: A pretty surface with surprising symmetry)
Dan Asimov <dasimov@earthlink.net> wrote:
Or consider the number 73. Not particularly conducive to symmetry, you might think.
73 is a palindrome in Morse Code: --... ...-- It's also a common greeting among hams.
On Sun, 1 Nov 2020, 19:08 Keith F. Lynch wrote:
Dan Asimov wrote:
Or consider the number 73. Not particularly conducive to symmetry, you might think.
73 is a palindrome in Morse Code: --... ...--
This Morse code symmetry comes from the base-10 complement palindromic symmetry, n = reverse (c10 (n)) where c10 := d |-> 10 - d digit-wise (ill defined for d = 0). Similar complement-palindromes are 5, 19, 28, 37, ..., *73*, 82, 91,159, 258, ..., 1199, 1289, ... See oeis.org/A299539 (added in 2018). The Morse-palindromic numbers are exactly these plus those of odd length with the middle 5 replaced by a 0. - Maximilan
Fans of the Big Bang Theory will recall that 73 is also Sheldon Cooper's favorite number. Apparently, this is because 73 is a prime number, its index in the sequence of primes is the product of its digits, namely 21, and upon reversing the digits of 73, one obtains the prime 37, which is the 12th prime, and 12 is the reverse of 21. A prime number satisfying these properties is called a Sheldon prime and a paper in the American Mathematical Monthly from 2019 proves that 73 is the only such prime. Proof of the Sheldon Conjecture | | | | | | | | | | | Proof of the Sheldon Conjecture Carl Pomerance (2019). Proof of the Sheldon Conjecture. The American Mathematical Monthly: Vol. 126, No. 8, pp. 688-698. | | | Best,Richard On Monday, November 2, 2020, 12:55:22 PM PST, M F Hasler <mhasler@dsi972.fr> wrote: On Sun, 1 Nov 2020, 19:08 Keith F. Lynch wrote:
Dan Asimov wrote:
Or consider the number 73. Not particularly conducive to symmetry, you might think.
73 is a palindrome in Morse Code: --... ...--
This Morse code symmetry comes from the base-10 complement palindromic symmetry, n = reverse (c10 (n)) where c10 := d |-> 10 - d digit-wise (ill defined for d = 0). Similar complement-palindromes are 5, 19, 28, 37, ..., *73*, 82, 91,159, 258, ..., 1199, 1289, ... See oeis.org/A299539 (added in 2018). The Morse-palindromic numbers are exactly these plus those of odd length with the middle 5 replaced by a 0. - Maximilan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
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Keith F. Lynch -
M F Hasler -
Richard Chatwin