A073064 Primes with non-distinct digits.

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

Author

Zak Seidov, Aug 24 2002

Keywords

• easy
• base
• nonn

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)

Examples

			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.
		

Crossrefs

Cf. A000040, A030291, A073069, A109303.

Programs

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]]]