

A217297


Triprimes that become cubes when their central digit (or central pair of digits) is deleted.


1



207, 604, 654, 2007, 2037, 2057, 2067, 2097, 2107, 2197, 2247, 2337, 2367, 2387, 2397, 2527, 2547, 2597, 2607, 2637, 2667, 2697, 2717, 2737, 2817, 2847, 2877, 2937, 2967, 6014, 6034, 6044, 6054, 6094, 6114, 6124, 6154, 6194, 6214, 6234, 6254, 6284, 6294, 6394
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

In theory, a cube with an even number of digits could be represented in the sequence by up to 110 numbers by inserting {0,9} and {00,99}. In the first 10000 terms, 1079^3 has a record 46 representatives, though it is unlikely that this is a global record.
The cubes of 10, 20 and 48 are the first three cubes not represented in the sequence.


LINKS

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) = 207 = 3*3*23, and becomes the cube 27 when the central digit is deleted.
a(4) = 2007 = 3*3*223, and becomes the cube 27 when the two central digits are deleted.


PROG

(R)library(gmp);
removecentraldigit<function(x) { s=as.character(x); n=nchar(s);
as.bigz(paste(substr(s, 1, ifelse(n%%2==0, n/21, (n1)/2)), substr(s, ifelse(n%%2==0, n/2+2, (n+3)/2), n), sep=""))};
istriprime=function(x) ifelse(as.bigz(x)<8, F, length(factorize(x))==3);
iscube<function(x) ifelse(as.bigz(x)<2, T, all(table(as.numeric(factorize(x)))%%3==0));
which(sapply(201:6400, function(x) istriprime(x) & iscube(removecentraldigit(x))))+200


CROSSREFS

Cf. A014612, A225082, A080603, A000578.
Sequence in context: A179171 A204876 A204869 * A205198 A205194 A204868
Adjacent sequences: A217294 A217295 A217296 * A217298 A217299 A217300


KEYWORD

nonn,base,less


AUTHOR

Kevin L. Schwartz and Christian N. K. Anderson, May 03 2013


STATUS

approved



