A298943 Lower of two consecutive Mersenne prime exponents with record first difference.

2, 3, 7, 19, 31, 127, 607, 1279, 2281, 3217, 4423, 11213, 23209, 44497, 132049, 216091, 1398269, 3021377, 6972593, 13466917, 43112609

Offset: 1

Author

Felix Fröhlich, Jan 30 2018

Keywords

• nonn
• hard
• more

Comments

A000043(i) is a term iff A134458(i) is a new record in A134458.

Conjecture: The sequence is infinite.

Examples

			A000043(7) = 19 and A134458(7) = 12, which is larger than A134458(i) for any i < 7, so 19 is a term of the sequence.
		

Links

• Wikipedia, Mersenne conjectures - Lenstra-Pomerance-Wagstaff conjecture.

Crossrefs

Cf. A000043, A134458.

Programs

Mathematica

Block[{s = Partition[MersennePrimeExponent@ Range@ 45, 2, 1], t}, t = Map[Differences, s][[All, 1]]; Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]][[All, 1]] (* Michael De Vlieger, Jan 31 2018 *)

PARI

LL(e) = my(n, h); n = 2^e-1; h = Mod(2, n); for (k=1, e-2, h=2*h*h-1); return(0==h) \\ after Joerg Arndt in A000043
my(r=0, p=2); forprime(q=3, , if(LL(q), if(q-p > r, print1(p, ", "); r=q-p); p=q))

Extensions

a(21) from Amiram Eldar, Oct 17 2024