A134039 -id:A134039 - 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

A134037 Concatenated first and last digits of Mersenne prime reversals.

Original entry on oeis.org

33, 77, 13, 71, 18, 11, 75, 72, 12, 16, 71, 71, 16, 75, 71, 71, 14, 12, 11, 72, 14, 13, 12, 14, 14, 14, 18, 75, 75, 15, 77, 71, 11, 74, 18, 16, 11, 14, 19, 71, 72, 71, 13, 11, 72, 11, 13

Offset: 1

Enoch Haga, Oct 02 2007

Not all reversals of Mersenne primes are primes. Concatenation is a convenient way to see whether the prime reversal might be prime (obviously not if ending in an even number or 5).

			a(4)=71 because the first and last digits of the 4th Mersenne prime 127 are 1 and 7. Reversed they are 7 and 1 and concatenated for convenience, 71.

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

Cf. A134038 A134039.

f[n_] := FromDigits[Part[IntegerDigits[n], {-1, 1}]]; f /@ (2^ MersennePrimeExponent[Range[47]] - 1) (* Amiram Eldar, Feb 16 2020 *)

Generate the Mersenne prime sequence. Reverse the primes. Find the value of the first and last digits and concatenate.

a(21)-a(47) from 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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A134037 Concatenated first and last digits of Mersenne prime reversals.

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

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PARI