A217256 - OEIS

%I #14 May 06 2013 11:23:16

%S 116,186,245,255,275,285,316,356,366,429,604,654,801,861,1066,1076,

%T 1086,1106,1146,1166,1246,1266,1396,1406,1426,1436,1446,1506,1516,

%U 1526,1556,1586,1606,1626,1636,1676,1686,1756,1786,1796,1826,1846,1866,1886,1916,1946

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

%C 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).

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

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

%H Christian N. K. Anderson, <a href="/A217256/b217256.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%o (R)library(gmp);

%o removecentraldigit<-function(x) { s=as.character(x); n=nchar(s);

%o     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=""))};

%o istriprime=function(x) ifelse(as.bigz(x)<8,F,length(factorize(x))==3);

%o issquare<-function(x) ifelse(x<2,T,all(table(as.numeric(factorize(x)))%%2==0))

%o which(sapply(101:1500,function(x) istriprime(x) & issquare(removecentraldigit(x))))+100

%Y Cf. A014612, A225082, A080603, A000290.

%K nonn,base,less

%O 1,1

%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 03 2013