login
A298943
Lower of two consecutive Mersenne prime exponents with record first difference.
0
2, 3, 7, 19, 31, 127, 607, 1279, 2281, 3217, 4423, 11213, 23209, 44497, 132049, 216091, 1398269, 3021377, 6972593, 13466917, 43112609
OFFSET
1,1
COMMENTS
A000043(i) is a term iff A134458(i) is a new record in A134458.
Conjecture: The sequence is infinite.
EXAMPLE
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.
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 *)
PROG
(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))
CROSSREFS
Sequence in context: A128025 A092064 A152609 * A340281 A172461 A253971
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, Jan 30 2018
EXTENSIONS
a(21) from Amiram Eldar, Oct 17 2024
STATUS
approved