OFFSET
1,1
COMMENTS
"Substrings" includes the whole number in itself.
The terms up to 11317 are primes themselves. The subsequence A168169 lists primes which have more than 2d prime substrings.
From Robert Israel, Nov 11 2020: (Start)
Palindromes in the sequence include 1337331, 1375731, and 1793971.
Even numbers in the sequence include 313732, 313792 and 1131712. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..2500
EXAMPLE
The least number with d digits to have 2d distinct prime substrings is a(1)=1373, with 4 digits and #{3, 7, 13, 37, 73, 137, 373, 1373} = 8.
MAPLE
filter:= proc(n) local i, j, count, d, S, x, y;
d:= ilog10(n)+1;
count:= 0; S:= {};
for i from 0 to d-1 do
x:= floor(n/10^i);
for j from i to d-1 do
y:= x mod 10^(j-i+1);
if not member(y, S) and isprime(y) then count:= count+1; S:= S union {y}; if count = 2*d then return true fi fi
od od;
false
end proc:
select(filter, [$10..10^5]); # Robert Israel, Nov 11 2020
PROG
(PARI) {for( p=1, 1e6, #prime_substrings(p) >= #Str(p)*2 & print1(p", "))} /* see A168168 for prime_substrings() */
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 28 2009
STATUS
approved