login
A057630
Primes such that replacing each digit d with d copies of the digit d produces a prime. Zeros are allowed.
3
11, 31, 53, 101, 131, 149, 223, 283, 311, 313, 331, 397, 463, 503, 641, 691, 937, 941, 1031, 1049, 1069, 1301, 1409, 1439, 1511, 1609, 1741, 1871, 1949, 1993, 1999, 2083, 2111, 2203, 2447, 2803, 2939, 3001, 3011, 3061, 3163, 3301, 3391, 3433, 3499, 3559
OFFSET
1,1
COMMENTS
"Replacing each digit d with d copies of the digit d" is the function A048376, well defined on the set of positive integers. Therefore (the range of) the present sequence is the largest subset of A000040 stable under the operation A048376.
A004022 is a subsequence. - Chai Wah Wu, Dec 19 2019
EXAMPLE
E.g. 641 becomes 66666644441 which is also prime.
MATHEMATICA
Select[Prime[Range[500]], PrimeQ[FromDigits[Flatten[Table[#, {#}]&/@ IntegerDigits[ #]]]]&] (* Harvey P. Dale, Dec 18 2010 *)
PROG
(PARI) is_A057630(n)={isprime(A048376(n)) && isprime(n)} \\ M. F. Hasler, Jan 23 2013
(Python)
from sympy import isprime, nextprime
A057630_list, dlist, p = [], [str(d)*d for d in range(10)], 2
while len(A057630_list) < 10000:
if isprime(int(''.join(dlist[int(d)] for d in str(p)))):
A057630_list.append(p)
p = nextprime(p) # Chai Wah Wu, Dec 19 2019, corrected Jan 01 2022
CROSSREFS
Sequence in context: A031287 A230329 A232764 * A057628 A144364 A226922
KEYWORD
nonn,base,nice,easy
AUTHOR
G. L. Honaker, Jr., Oct 10 2000
EXTENSIONS
More terms from Patrick De Geest, Oct 15 2000
Offset changed to 1, according to OEIS conventions, by M. F. Hasler, Jan 23 2013
STATUS
approved