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

1,1

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)

Links

Table of n, a(n) for n=1..50.

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

Cf. A000040, A030291, A073069, A109303.

Sequence in context: A305395 A158051 A091366 * A155075 A180421 A176179

Adjacent sequences: A073061 A073062 A073063 * A073065 A073066 A073067

Keyword

easy,base,nonn

Author

Zak Seidov, Aug 24 2002

Status

approved