A167992 Least n-digit emirp (A006567) with emirp digital sum, or 0 if no such value.

0, 0, 157, 1097, 10039, 100129, 1000039, 10000169, 100000543, 1000000097, 10000000277, 100000000237, 1000000001159, 10000000000853, 100000000001173, 1000000000000273, 10000000000000079, 100000000000001249

Offset: 1

Author

Jonathan Vos Post, Nov 16 2009

Keywords

• base
• nonn

Comments

Least emirp (non-palindromic prime in A007500, i.e., prime whose reversal is a different prime) greater than 10^n, for which the sum of digits (A007953) is also an emirp.

Examples

			a(1) = a(2) = 0. a(3) = 157 because 157 is the least non-palindromic prime p > 10^3 such that R(p), in this case 751, is also prime, and the sum of digits sod(p), in this case 1+5+7 = 13, is likewise an emirp (prime with reversal a different prime). a(4) = 1097 because it is the smallest 4-digit prime, whose reversal (7901) is a different prime, and whose digital sum 1+0+9+7 = 17, which is prime and has a prime reversal (71).
		

Crossrefs

Cf. A000040, A004086, A007500, A006567, A114018.

Programs

Maple

read("transforms") ; A007953 := proc(n) local d ; add(d, d=convert(n,base,10)) ; end proc: isA006567 := proc(p) if isprime(p) then isprime(digrev(p)) and digrev(p) <> p ; else false ; end if; end proc ; A167992 := proc(n) local p; p := nextprime(10^(n-1)) ; while p <= 10^n do if isA006567(p) and isA006567(A007953(p)) then return p; end if; p := nextprime(p) ; end do ; return 0 ; end proc: seq(A167992(n),n=1..70) ; # R. J. Mathar, Nov 18 2009

Formula

a(n) = Min{p > 10^n in A006567, and A007953(p) is in A006567} = Min{p > 10^n in A000040 such that A004086(p) is in A000040, and A004086(p) distinct from p, and in A006567(p) is in A000040, and A004086(p) distinct from A006567(p), and in A000040}.

Extensions

More terms from R. J. Mathar, Nov 18 2009