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

Author

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

Keywords

• nonn
• base
• less

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A014612, A225082, A080603, A000290.

Programs

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