A334092 Primes p of the form of the form q*2^h + 1, where q is one of the Fermat primes; Primes p for which A329697(p) == 2.

7, 11, 13, 41, 97, 137, 193, 641, 769, 12289, 40961, 163841, 557057, 786433, 167772161, 2281701377, 3221225473, 206158430209, 2748779069441, 6597069766657, 38280596832649217, 180143985094819841, 221360928884514619393, 188894659314785808547841, 193428131138340667952988161

Offset

1,1

Comments

Primes p such that p-1 is not a power of two, but for which A171462(p-1) = (p-1-A052126(p-1)) is [a power of 2].

Primes of the form ((2^(2^k))+1)*2^h + 1, where ((2^(2^k))+1) is one of the Fermat primes, A019434, 3, 5, 17, 257, ..., .

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..53

Prog

(PARI) isA334092(n) = (isprime(n)&&2==A329697(n));
(PARI)
A052126(n) = if(1==n, n, n/vecmax(factor(n)[, 1]));
A209229(n) = (n && !bitand(n, n-1));
isA334092(n) = (isprime(n)&&(!A209229(n-1))&&A209229(n-1-A052126(n-1)));
(PARI) list(lim)=if(exponent(lim\=1)>=2^33, error("Verify composite character of more Fermat primes before checking this high")); my(v=List(), t); for(e=0, 4, t=2^2^e+1; while((t<<=1)<lim, if(isprime(t+1), listput(v, t+1)))); Set(v) \\ Charles R Greathouse IV, Apr 14 2020

Crossrefs

Primes in A334102.

Intersection of A081091 and A147545.

Subsequences: A039687, A050526, A300407.

Cf. A000040, A010051, A019434, A052126, A171462, A329697. Cf. also A334093, A334094, A334095, A334096.

Sequence in context: A330699 A084457 A045460 * A054299 A116442 A191083

Adjacent sequences: A334089 A334090 A334091 * A334093 A334094 A334095

Keyword

nonn

Author

Antti Karttunen, Apr 14 2020

Extensions

More terms from Giovanni Resta, Apr 14 2020

Status

approved