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A073064
Primes with non-distinct digits.
2
11, 101, 113, 131, 151, 181, 191, 199, 211, 223, 227, 229, 233, 277, 311, 313, 331, 337, 353, 373, 383, 433, 443, 449, 499, 557, 577, 599, 661, 677, 727, 733, 757, 773, 787, 797, 811, 877, 881, 883, 887, 911, 919, 929, 977, 991, 997, 1009, 1013, 1019
OFFSET
1,1
COMMENTS
A000040 INTERSECT A109303. - R. J. Mathar, May 01 2008
Comment from N. J. A. Sloane, Jan 22 2023 (Start)
A "nontrivial permutation" means any one of the m!-1 elements of S_m apart from the identity permutation.
This sequence consists of those primes that are fixed under at least one nontrivial permutation of its digits.
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)
EXAMPLE
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.
MAPLE
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
MATHEMATICA
ta=IntegerDigits[Prime[Range[1000]]]; ta2=Table[Length[ta[[i]]]>Length[Union[ta[[i]]]], {i, 1000}]; Prime[Flatten[Position[ta2, True]]]
CROSSREFS
KEYWORD
easy,base,nonn
AUTHOR
Zak Seidov, Aug 24 2002
STATUS
approved