A173595 The smaller member of a near-repdigit emirp pair.

113, 199, 337, 1151, 1181, 3343, 3373, 7177, 7577, 11161, 77797, 98999, 111119, 111211, 323333, 333337, 333433, 777787, 777877, 991999, 1111711, 3333373, 9929999, 11111117, 11111911, 11113111

Offset: 1

Author

Lekraj Beedassy, Feb 22 2010

Keywords

• base
• nonn

Comments

a(n) and an associated A173596 = A004086(a(n)) are a near-repdigit emirp pair, and all these pairs united, sorted, generate A173594.

Examples

			a(3) = 337 and A173596(2) = 733 are an emirp pair using only two different digits.
		

Crossrefs

Cf. A173594, A173596.

Programs

Maple

read("transforms") ; isA164937 := proc(n) local dse ; if isprime(n) and n > 100 then dse := convert(convert(n,base,10),multiset) ; if nops(dse) = 2 then op(2,op(1,dse)) = 1 and op(2,op(2,dse)) > 1 or op(2,op(1,dse)) > 1 and op(2,op(2,dse)) = 1; else false; end if ; else false; end if; end proc:
isA006567 := proc(n) if isprime(n) then pr := digrev(n) ; return isprime(pr) and pr <> n ; else false; end if; end proc:
isA173594 := proc(n) isA164937(n) and isA006567(n) ; end proc:
isA173595 := proc(n) return isA173594(n) and digrev(n) > n end proc:
for n from 2 do if isA173595(n) then printf("%d,",n) ; fi ; end do ; # R. J. Mathar, Mar 05 2010

Extensions

Keyword:base added by R. J. Mathar, Feb 24 2010, Mar 05 2010