login
A241019
a(n) is the smallest j such that the n-digit number consisting of a 1 in position j and 3's in the other n-1 positions is a prime, or 0 if no such prime exists.
6
1, 2, 3, 2, 2, 4, 2, 6, 5, 5, 5, 0, 3, 8, 1, 11, 7, 6, 4, 5, 11, 5, 0, 0, 9, 11, 0, 5, 5, 0, 4, 5, 17, 19, 19, 6, 0, 3, 9, 35, 1, 27, 24, 32, 0, 36, 14, 11, 34, 14, 22, 0, 17, 53, 0, 47, 11, 0, 16, 3, 0, 15, 0, 39, 22, 40, 27, 39, 0, 19, 2, 19, 48, 2, 43, 19
OFFSET
2,2
COMMENTS
Previous name: Let x(1)x(2)... x(n) denote the decimal expansion of a number p having an index j such that x(j) = 1 and x(i) = 3 for i <> j. The sequence lists the smallest index j such that p is prime, or 0 if no such prime exists.
Except 0, the corresponding primes are 13, 313, 3313, 31333, 313333, 3331333, 31333333, 333331333, 3333133333, 33331333333, 333313333333, 0, 33133333333333, ... .
LINKS
MAPLE
with(numtheory):nn:=80:T:=array(1..nn):
for n from 2 to nn do:
for i from 1 to n do:
T[i]:=3:
od:
ii:=0:
for j from 1 to n while(ii=0)do:
T[j]:=1:s:=sum('T[i]*10^(n-i)', 'i'=1..n):
if type(s, prime)=true
then
ii:=1: printf(`%d, `, j):
else
T[j]:=3:
fi:
od:
if ii=0
then
printf(`%d, `, 0):
else
fi:
od:
PROG
(Python)
from sympy import isprime
def a(n):
base = (10**n-1)//9*3
for j in range(1, n+1):
t = base - 2*10**(n-j)
if isprime(t):
return j
return 0
print([a(n) for n in range(2, 78)]) # Michael S. Branicky, Jun 02 2024
CROSSREFS
Sequence in context: A375341 A368039 A160558 * A023581 A023574 A210941
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 15 2014
EXTENSIONS
Name simplified and offset corrected by Michael S. Branicky, Jun 02 2024
STATUS
approved