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%I #14 Apr 21 2024 13:23:26
%S 4,6,7,11,12,14,15,16,19,22,28,29,30
%N Mersenne indices of Mersenne prime reversals which are odd composites (associated with A134039).
%C Suggested by Puzzle 417 of Carlos Rivera's The Prime Puzzles & Problems Connection The program below, slightly modified, was used to find the first prime divisor of the Mersenne reversal if an odd composite
%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_417.htm">Puzzle 417. M(e) reversed primes</a>, The Prime Puzzles & Problems Connection.
%F Generate the Mersenne primes, reverse; if the reversal is an odd composite find the first prime divisor associated with the Mersenne index number
%e The Mersenne index 4 is that of 2^7-1 = 127. The reversal is 721 whose first prime divisor is 7 and 7*103=721.
%t rev[n_] := FromDigits @ Reverse @ IntegerDigits[n]; oddComp[n_] := OddQ[n] && CompositeQ[n]; Select[Range[20], oddComp[rev[2^MersennePrimeExponent[#] - 1]] &] (* _Amiram Eldar_, Feb 16 2020 *)
%o (UBASIC)
%o 05 'for a(4):
%o 10 'primes using counters
%o 20 N=727501488517303786137132964064381141071
%o 30 A=3:S=sqrt(N):C="c"
%o 40 B=N\A
%o 50 if B*A=N then print B;A;N;"-";:N=N+2:goto 30
%o 60 A=A+2
%o 70 if A<=sqrt(N) then 40
%o 80 if N>2 then stop 81 C=C+1
%o 90 print C;N;"-";
%o 100 N=N+2:goto 30
%Y Cf. A000043, A134037, A134039.
%K nonn,base,more,changed
%O 1,1
%A _Enoch Haga_, Oct 02 2007
%E a(3) inserted and a(6)-a(13) added by _Amiram Eldar_, Feb 16 2020
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