A238362 Primes p such that A000120(p - 1) = A000120(p + 1) = 2^k for some k.

3, 11, 19, 59, 67, 107, 131, 179, 211, 227, 283, 307, 331, 419, 563, 587, 659, 787, 1019, 1051, 1123, 1163, 1171, 1187, 1291, 1531, 1571, 1667, 1787, 1979, 2011, 2027, 2099, 2131, 2243, 2339, 2371, 2579, 2819, 2939, 3083, 3203, 3323, 3331, 3547, 3571, 3803

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

3 is in this sequence because A000120(3-1) = A000120(3+1) = 2^0 = 1.

Mathematica

Select[Prime[Range[500]], (s = DigitCount[#-1, 2, 1]) == DigitCount[#+1, 2, 1] && s == 2^IntegerExponent[s, 2] &] (* Amiram Eldar, Jul 16 2023 *)

Prog

(PARI) ispow2(n)=n>>=valuation(n, 2); n==1
is(n)=my(h=hammingweight(n-1)); ispow2(h) && h==hammingweight(n+1) && isprime(n) \\ Charles R Greathouse IV, Mar 05 2014

Crossrefs

Cf. A000120.

Sequence in context: A336790 A163851 A213051 * A116945 A048270 A183459

Adjacent sequences: A238359 A238360 A238361 * A238363 A238364 A238365

Keyword

nonn,base

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Feb 25 2014

Extensions

2311 removed by Giovanni Resta, Mar 01 2014

Status

approved