A134039 First prime divisor of odd composite Mersenne prime reversals.

7, 13, 5, 47, 683, 5, 20149, 19, 2399, 15383, 5, 5, 5

Offset: 1

Author

Enoch Haga, Oct 02 2007

Keywords

• nonn
• base
• more

Comments

The UBASIC program below was used to find a(3)=683. Suggested by Puzzle 417, Carlos Rivera's The Prime Puzzles & Problems Connection (puzzle inspired by G. L. Honaker, Jr.'s Prime Curios)

Examples

			a(2) = 13 because the 6th Mersenne prime is 2^17-1 = 131071. Reversed this number is 170131, which is equal to 13*13087.
		

Links

• Carlos Rivera, Puzzle 417. M(e) reversed primes, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A134037, A134038.

Programs

Mathematica

rev[n_] := FromDigits@Reverse@IntegerDigits[n]; lpf[n_] := Module[{p = 2}, While[! Divisible[n, p], p = NextPrime[p]]; p]; seq={}; Do[r = rev[2^MersennePrimeExponent[n] - 1]; p = lpf[r]; If[p > 2 && p < r, AppendTo[seq, p]], {n, 1, 30}]; seq (* Amiram Eldar, Feb 16 2020 *)

UBASIC

to find a(3)=683. 10 'primes using counters 20 N=727501488517303786137132964064381141071 30 A=3:S=sqrt(N):C="c" 40 B=N\A 50 if B*A=N then print B;A;N;"-";:N=N+2:goto 30 60 A=A+2 70 if A<=sqrt(N) then 40 80 if N>2 then stop 81 C=C+1 90 print C;N;"-"; 100 N=N+2:goto 30

Formula

Generate the sequence of Mersenne primes, reverse each and test for primality. If the reversal is an odd composite, find the first prime divisor.

Extensions

a(3) inserted and a(6)-a(13) added by Amiram Eldar, Feb 16 2020