A168110 Palindromic primes in base 8 which are also emirps (A006567) in base 10.

73, 97, 113, 12547, 12611, 13259, 13523, 14107, 14563, 14891, 15667, 15731, 30367, 31799, 31991, 312073, 318281, 350033, 359377, 366169, 371353, 372377, 383833, 392153, 393761, 397921, 792131, 796291, 936227, 936739, 948707, 966379, 992947, 1005427, 1008563, 1029883, 1043899, 1048571, 1311749, 1313797, 1340357, 1358029

Offset: 1

Author

Jonathan Vos Post, Nov 18 2009

Keywords

• base
• nonn

Comments

What is a good way in the OEIS to show other such pairs of bases analogous to this?

Examples

			a(1) = 73 because 73 (base 8) = 111 (which is a palindrome), and R(73) = 37 which is a different prime (base 10). a(2) = 97 because 97 (base 8) = 141 (which is a palindrome), and R(97) = 79 which is a different prime (base 10). a(3) = 113 because 113 (base 8) = 161 (which is a palindrome), and R(113) = 311 which is a different prime (base 10). a(4) = 12547 because 12547 (base 8) = 30403 (which is a palindrome), and R(12547) = 74521 which is a different prime (base 10).
		

Crossrefs

Cf. A000040, A004086, A006567, A007094, A029976.

Programs

Maple

isA006567 := proc(p) local r; if isprime(p) then r := digrev(p) ; r <> p and isprime(r) ; else false; end if; end proc: isA029803 := proc(n) local dgs,d; dgs := convert(n,base,8) ; for d from 1 to nops(dgs)/2 do if op(d,dgs) <> op(-d,dgs) then return false; end if; end do ; return true; end proc: isA029976 := proc(n) isprime(n) and isA029803(n) ; end proc: isA168110 := proc(p) isA029976(p) and isA006567(p) ; end proc: A168110 := proc(n) option remember ; local a; if n = 1 then 73 ; else a := nextprime(procname(n-1)) ; while not isA168110(a) do a := nextprime(a) ; end do ; return a; end if; end proc: seq(A168110(n),n=1..30) ; # R. J. Mathar, Dec 06 2009

Mathematica

okQ[n_]:=Module[{fridn=FromDigits[Reverse[IntegerDigits[n]]], idn8= IntegerDigits[n,8]}, fridn!=n&&PrimeQ[fridn]&&idn8==Reverse[idn8]]; Select[Prime[Range[75000]],okQ] (* Harvey P. Dale, Aug 10 2011 *)

Formula

A029976 INTERSECTION A006567.

Extensions

Terms beyond a(10) by R. J. Mathar, Dec 06 2009