A134039 First prime divisor of odd composite Mersenne prime reversals.

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

Offset

1,1

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)

Links

Table of n, a(n) for n=1..13.

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

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.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A134037, A134038.

Sequence in context: A352171 A225091 A225516 * A125741 A103705 A157517

Adjacent sequences: A134036 A134037 A134038 * A134040 A134041 A134042

Keyword

nonn,base,more

Author

Enoch Haga, Oct 02 2007

Extensions

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

Status

approved