Volker Diels-Grabsch - cp's OEIS frontend

User: Volker Diels-Grabsch

Volker Diels-Grabsch has authored 2 sequences.

A278316 Odd numbers n such that q(n)^2 = q(n^2) != 0, where q(n) is the digit product on base 10.

1, 3, 661, 983, 2631, 2893, 12385, 12893, 14661, 18615, 27519, 35383, 36213, 38691, 46215, 49231, 83631, 87291, 92843, 113865, 116683, 123415, 129815, 136423, 139261, 152619, 161683, 162435, 166817, 178119, 194725, 244635, 247941, 254663, 274165, 276941

Offset: 1

Volker Diels-Grabsch, Nov 18 2016

			For n=3, a(3)=661: q(661)^2 = (6*6*1)^2 = 36^2 = 1296 = 4*3*6*9*2*1 = q(436921) = q(661^2).

Michael Huke, Solution to exercise psi-15 (German language article), WURZEL 11/2016, November 2016, page 252, http://wurzel.org/

Odd terms of A256115. - Michel Marcus, Dec 04 2016

Select[Range[1, 10^6, 2], And[MatchQ @@ #, Times @@ # != 0] &@{(Times @@ IntegerDigits@ #)^2, Times @@ IntegerDigits[#^2]} &] (* Michael De Vlieger, Dec 06 2016 *)

pd(n) = my(d=digits(n)); prod(k=1, #d, d[k]);
isok(n) = (n % 2) && (p = pd(n)^2) && (p == pd(n^2)); \\ Michel Marcus, Dec 04 2016

More terms from Jon E. Schoenfield, Dec 02 2016

A228162 Number of bangbangs (!!) in shell substitution when starting with : '!!' and : "!!" '!!'.

Original entry on oeis.org

1, 2, 2, 3, 5, 17, 161, 15681, 159591041, 16866847940875521, 189345699699803478502456213711361

Offset: 0

Volker Diels-Grabsch, Aug 16 2013

nonn

Executing the following no-op commands in a unix shell (bash, dash or zsh)
: '!!'
: "!!" '!!'
followed by repeated execution of the last command (arrow-up, enter) leads to a series of substitutions due to the !! (bangbang) operator:
: ": '!!'" '!!'
: ": ': ": '!!'" '!!''" '!!'
: ": ': ": '!!'" ': ": ': ": '!!'" '!!''" '!!'''" '!!'
These commands show a very irregular pattern as some of the single-quotes (') and double quotes(") switch their role from string delimiters to string contents and vice versa.
Also, these commands grow very fast. After a few repetitions, they'll quickly fill the RAM as well as the hard disk (because of the command history file).
This sequence describes the number of bangbangs (!!) of each command.

			For n = 4 the value a(4) = 5 is the number of bangbangs (!!) in the following command:
: ": ': ": '!!'" ': ": ': ": '!!'" '!!''" '!!'''" '!!'

Volker Diels-Grabsch, Table of n, a(n) for n = 0..14
Shadab Ahmed, Bang Bang !!
Robin Houston, The algebra of Unix command substitution

for i, ai in enumerate([1, 2, 2, 3, 5]):
    print('%d %d' % (i, ai))
p, q = 2, 4
for i in range(5, 15):
    print('%d %d' % (i, 4*p + 2*q + 1))
    p, q = 3*p*p + 2*p + p*q, 2*p*p + 2*p*q + 2*q

a(0) = 1, a(1) = 2, a(2) = 2, a(3) = 3, a(4) = 5, and for n >= 5, a(n) = 4*p(n) + 2*q(n) + 1 where p(5) = 2, q(5) = 4, and p(n+1) = 3*p(n)^2 + 2*p(n) + p(n)*q(n) and q(n+1) = 2*p(n)^2 + 2*p(n)*q(n) + 2*q(n).

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User: Volker Diels-Grabsch

A278316 Odd numbers n such that q(n)^2 = q(n^2) != 0, where q(n) is the digit product on base 10.

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A228162 Number of bangbangs (!!) in shell substitution when starting with : '!!' and : "!!" '!!'.

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