A217256 Triprimes that become squares when their central digit (or central pair of digits) is deleted.

116, 186, 245, 255, 275, 285, 316, 356, 366, 429, 604, 654, 801, 861, 1066, 1076, 1086, 1106, 1146, 1166, 1246, 1266, 1396, 1406, 1426, 1436, 1446, 1506, 1516, 1526, 1556, 1586, 1606, 1626, 1636, 1676, 1686, 1756, 1786, 1796, 1826, 1846, 1866, 1886, 1916, 1946

Offset

1,1

Comments

In theory, every square number potentially could have 110 triprime representatives through the insertion of 0-9, and 00-99. It appears 25, which is represented by 48 entries in the sequence, holds the record (confirmed for squares < 594441).

1600 is the first valid square number (with an even number of digits) not represented in the sequence.

104976 is the first valid square number not divisible by 100 with no representatives.

Links

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

Example

a(1)=116 and a(15)=1066 are both triprimes (2*2*29 and 2*13*41 respectively) and become the square number 16 upon deletion.

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/2-1, (n-1)/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);
issquare<-function(x) ifelse(x<2, T, all(table(as.numeric(factorize(x)))%%2==0))
which(sapply(101:1500, function(x) istriprime(x) & issquare(removecentraldigit(x))))+100

Crossrefs

Cf. A014612, A225082, A080603, A000290.

Sequence in context: A095623 A257197 A105934 * A179168 A259584 A184069

Adjacent sequences: A217253 A217254 A217255 * A217257 A217258 A217259

Keyword

nonn,base,less

Author

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

Status

approved