

A134039


First prime divisor of odd composite Mersenne prime reversals.


3



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



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 2^171 = 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



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS

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


STATUS

approved



