cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

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Author

Enoch Haga, Oct 02 2007

Keywords

Comments

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).

Examples

			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.

Links

Crossrefs

Cf. A134038 A134039.

Programs

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

Formula

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

Extensions

a(21)-a(47) from 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

Views

Author

Enoch Haga, Oct 02 2007

Keywords

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)

Examples

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

Links

Crossrefs

Cf. A134037, A134038.

Programs

  • 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 *)
  • 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

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.

Extensions

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

Views

Author

Metin Sariyar, Aug 09 2019

Keywords

Comments

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.

Examples

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

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[7667], PrimeQ[IntegerReverse[2^# - 1]] &]
  • PARI
    isok(k) = isprime(fromdigits(Vecrev(digits(2^k-1)))); \\ Michel Marcus, Aug 10 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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