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%I #30 Jan 01 2022 21:22:31
%S 11,31,53,101,131,149,223,283,311,313,331,397,463,503,641,691,937,941,
%T 1031,1049,1069,1301,1409,1439,1511,1609,1741,1871,1949,1993,1999,
%U 2083,2111,2203,2447,2803,2939,3001,3011,3061,3163,3301,3391,3433,3499,3559
%N Primes such that replacing each digit d with d copies of the digit d produces a prime. Zeros are allowed.
%C "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.
%C A004022 is a subsequence. - _Chai Wah Wu_, Dec 19 2019
%H Chai Wah Wu, <a href="/A057630/b057630.txt">Table of n, a(n) for n = 1..10000</a>
%e E.g. 641 becomes 66666644441 which is also prime.
%t Select[Prime[Range[500]],PrimeQ[FromDigits[Flatten[Table[#,{#}]&/@ IntegerDigits[ #]]]]&] (* _Harvey P. Dale_, Dec 18 2010 *)
%o (PARI) is_A057630(n)={isprime(A048376(n)) && isprime(n)} \\ _M. F. Hasler_, Jan 23 2013
%o (Python)
%o from sympy import isprime, nextprime
%o A057630_list, dlist, p = [], [str(d)*d for d in range(10)], 2
%o while len(A057630_list) < 10000:
%o if isprime(int(''.join(dlist[int(d)] for d in str(p)))):
%o A057630_list.append(p)
%o p = nextprime(p) # _Chai Wah Wu_, Dec 19 2019, corrected Jan 01 2022
%Y Cf. A004022, A057628.
%K nonn,base,nice,easy
%O 1,1
%A _G. L. Honaker, Jr._, Oct 10 2000
%E More terms from _Patrick De Geest_, Oct 15 2000
%E Offset changed to 1, according to OEIS conventions, by _M. F. Hasler_, Jan 23 2013
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