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Numbers k such that prime(k) can be written using only the digits of k (but they may used multiple times).
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%I #29 Sep 11 2022 19:00:58

%S 137,187,321,917,1098,1346,1347,1349,1362,1367,1384,1395,1528,1583,

%T 1850,1859,1876,1973,2415,2490,2517,2631,2632,2970,3417,3529,3573,

%U 3575,3590,3598,3751,3785,3860,4301,4537,4591,4639,4927,4980,4983,5231,5319,5342,5790,6106,6107

%N Numbers k such that prime(k) can be written using only the digits of k (but they may used multiple times).

%C The digits of k can be reused. In other words, the distinct digits of prime(k) form a subset of the set of the distinct digits of k.

%C This sequence is infinite as every pandigital number is in this sequence, see A171102.

%e The 137th prime number is 773, which can be written with the digits of 137. Thus 137 is in this sequence.

%t Select[Range[10000], SubsetQ[Sort[IntegerDigits[#]], Sort[IntegerDigits[Prime[#]]]] &]

%o (Python)

%o from sympy import nextprime

%o from itertools import count, islice

%o def agen(): # generator of terms

%o pk = 2

%o for k in count(1):

%o if set(str(pk)) <= set(str(k)): yield k

%o pk = nextprime(pk)

%o print(list(islice(agen(), 46))) # _Michael S. Branicky_, Sep 09 2022

%Y Cf. A171102, A080794.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Sep 09 2022