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A225082 Centrally deletable primes. 3
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 229, 233, 239, 263, 269, 283, 293, 307, 311, 317, 331, 337, 347, 367, 397, 401, 421, 431, 433, 443, 457, 461, 463, 467, 487, 491, 503, 509, 523, 563 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Prime numbers that remain primes when their central digit is (or two central digits are) deleted.
At the 1886th prime number (16229), there are exactly 943 centrally deletable primes, and 943 that become composites. It appears that there are always more non-deletable primes thereafter.
Subset of A080603 and of A077359.
LINKS
Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
EXAMPLE
a(5) = 1(1)3, and 13 is a prime.
MATHEMATICA
dcd[n_] := Block[{d = IntegerDigits@n, z}, z = Length@d; FromDigits@ Delete[d, Floor[(z + {{1}, {2}})/2]]]; Select[Prime@ Range@ 103, PrimeQ@ dcd@ # &] (* Giovanni Resta, Apr 29 2013 *)
PROG
(R) library(gmp)
sumsubstrpow<-function(n) {
no0<-function(s){ while(substr(s, 1, 1)=="0" && nchar(s)>1) s=substr(s, 2, nchar(s)); s}
tot=as.bigz(0); s=as.character(n); len=nchar(s)
for(i in 1:len) for(j in i:len) tot=tot+as.bigz(no0(substr(s, i, j)))^(j-i+1)
tot
}
#recursive
n=as.bigz(10); for(y in 1:4) n[y+1]=sumsubstrpow(n[y])
CROSSREFS
Sequence in context: A162199 A195469 A210758 * A327915 A131687 A327914
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)