A134037 -id:A134037 - cp's OEIS frontend

A134038 Mersenne indices of Mersenne prime reversals which are odd composites (associated with A134039).

4, 6, 7, 11, 12, 14, 15, 16, 19, 22, 28, 29, 30

Offset: 1

Enoch Haga, Oct 02 2007

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

			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.

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

Cf. A000043, A134037, A134039.

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 *)

05 'for a(4):
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

Generate the Mersenne primes, reverse; if the reversal is an odd composite find the first prime divisor associated with the Mersenne index number

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

A134039 First prime divisor of odd composite Mersenne prime reversals.

Original entry on oeis.org

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

Offset: 1

Enoch Haga, Oct 02 2007

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)

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

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

Cf. A134037, A134038.

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 *)

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

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

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

A309607 Exponents k for which reversal(2^k-1) is prime.

Original entry on oeis.org

2, 3, 5, 53, 189, 293, 1107, 2181, 2695, 2871, 7667, 19999, 27471, 44537, 62323, 134367, 174295

Offset: 1

Metin Sariyar, Aug 09 2019

According to the statements in the first link given below, the terms for k <= 7667, the primes of the form reversal(2^k-1) are certified and for k >= 19999 they are probable primes.

			5 is included because for n=5, reversal(2^5-1)=13 is prime.

Carlos Rivera, Puzzle 417.
Chris K. Caldwell and G. L. Honaker, Prime Curio for 1990474529917009.

Cf. A000225, A000668, A001348, A000079, A000043, A057708, A134037, A134038, A134039.

Select[Range[7667], PrimeQ[IntegerReverse[2^# - 1]] &]

isok(k) = isprime(fromdigits(Vecrev(digits(2^k-1)))); \\ Michel Marcus, Aug 10 2019

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A134038 Mersenne indices of Mersenne prime reversals which are odd composites (associated with A134039).

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A134039 First prime divisor of odd composite Mersenne prime reversals.

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Mathematica

UBASIC

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A309607 Exponents k for which reversal(2^k-1) is prime.

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Mathematica

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