A370606 Primes p such that valuation(p-1,2) is a record.

2, 3, 5, 17, 97, 193, 257, 7681, 12289, 40961, 65537, 786433, 5767169, 7340033, 23068673, 104857601, 167772161, 469762049, 2013265921, 3221225473, 75161927681, 77309411329, 206158430209, 2061584302081, 2748779069441, 6597069766657, 39582418599937, 79164837199873

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1770

Prog

(PARI) r=-1; forprime(p=2, 10^12, v=valuation(p-1, 2); if(v>r, print1(p, ", "); r=v))
(Python)
from itertools import count, islice
from sympy import isprime
def A370606_gen(): # generator of terms
    a = 1
    while True:
        for q in count(a, a):
            if isprime(q+1):
                yield q+1
                a = (q&-q)<<1
                break
A370606_list = list(islice(A370606_gen(), 30)) # Chai Wah Wu, Feb 23 2024

Crossrefs

Cf. A084924 (valuation(p+1,2) is a record).

Cf. A370607 (corresponding 2-valuations).

Sequence in context: A065952 A308316 A089983 * A072858 A276629 A218086

Adjacent sequences: A370603 A370604 A370605 * A370607 A370608 A370609

Keyword

nonn

Author

Joerg Arndt, Feb 23 2024

Extensions

a(21)-a(28) from Chai Wah Wu, Feb 23 2024

Status

approved