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%I #15 Jan 22 2023 12:28:23
%S 11,101,113,131,151,181,191,199,211,223,227,229,233,277,311,313,331,
%T 337,353,373,383,433,443,449,499,557,577,599,661,677,727,733,757,773,
%U 787,797,811,877,881,883,887,911,919,929,977,991,997,1009,1013,1019
%N Primes with non-distinct digits.
%C A000040 INTERSECT A109303. - _R. J. Mathar_, May 01 2008
%C Comment from _N. J. A. Sloane_, Jan 22 2023 (Start)
%C A "nontrivial permutation" means any one of the m!-1 elements of S_m apart from the identity permutation.
%C This sequence consists of those primes that are fixed under at least one nontrivial permutation of its digits.
%C A prime p is in the sequence iff its decimal expansion p = d_1 d_2 ... d_m is such that there is a non-identity permutation pi in S_m with the property that p = d_pi(1) d_pi(2) ... d_pi(m). (End)
%e a(1)=11 because 11 is the first prime not all digits of which are distinct; a(2)=101 because 101 is the second prime not all digits of which are distinct.
%p A055642 := proc(n) max(ilog10(n)+1,1) ; end: A043537 := proc(n) nops(convert(convert(n,base,10),set)) ; end: isA109303 := proc(n) RETURN( A055642(n) > A043537(n) ) ; end: isA073064 := proc(n) RETURN(isprime(n) and isA109303(n) ) ; end: for n from 1 to 1019 do if isA073064(n) then printf("%d,",n) ; fi ; od: # _R. J. Mathar_, May 01 2008
%t ta=IntegerDigits[Prime[Range[1000]]]; ta2=Table[Length[ta[[i]]]>Length[Union[ta[[i]]]], {i, 1000}]; Prime[Flatten[Position[ta2, True]]]
%Y Cf. A000040, A030291, A073069, A109303.
%K easy,base,nonn
%O 1,1
%A _Zak Seidov_, Aug 24 2002
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