A057630 Primes such that replacing each digit d with d copies of the digit d produces a prime. Zeros are allowed.

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

Author

G. L. Honaker, Jr., Oct 10 2000

Keywords

• nonn
• base
• nice
• easy

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

Examples

			E.g. 641 becomes 66666644441 which is also prime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004022, A057628.

Programs

Mathematica

Select[Prime[Range[500]],PrimeQ[FromDigits[Flatten[Table[#,{#}]&/@ IntegerDigits[ #]]]]&]  (* Harvey P. Dale, Dec 18 2010 *)

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

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