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 A227930 Primes p such that p-1 and p+1 have an even Hamming weight. 3
 11, 19, 47, 59, 67, 79, 107, 131, 179, 191, 211, 227, 239, 251, 271, 283, 307, 331, 367, 379, 419, 431, 443, 463, 491, 499, 563, 587, 659, 719, 787, 827, 859, 883, 911, 947, 971, 1019, 1039, 1051, 1087, 1123, 1163, 1171, 1187, 1231, 1259, 1279, 1291, 1327, 1423, 1451, 1459, 1471, 1483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes such that both neighbors are evil (as defined in A001969). From Antti Karttunen, Dec 29 2013: (Start) Excluding 2, the intersection of A027697 (Odious primes: primes with odd number of 1's in binary expansion) and A095282 (Primes whose binary-expansion ends with an even number of 1's). Equally, the intersection of A092246 (Odd "odious" numbers) and A095282. Equally, odd odious primes p such that A007814(p+1) is even. (End) LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 MAPLE read("transforms"): isA000069 := proc(n) if wt(n) mod 2 = 1 then true; else false; end if; end proc: for n from 1 do if isprime(n) and not isA000069(n-1) and not isA000069(n+1) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Oct 08 2013 (Scheme, with Antti Karttunen's IntSeq-library, two alternative implementations) (define A227930 (MATCHING-POS 1 1 (lambda (n) (and (even? (A000120 (- n 1))) (even? (A000120 (+ n 1))) (prime? n))))) (define A227930v2 (MATCHING-POS 1 1 (lambda (n) (and (odd? n) (odd? (A000120 n)) (even? (A007814 (+ n 1))) (prime? n))))) # Antti Karttunen, Dec 29 2013 MATHEMATICA Select[Prime[Range[250]], And @@ EvenQ[DigitCount[# + {-1, 1}, 2, 1]] &] (* Amiram Eldar, Jul 24 2023 *) PROG (PARI) is(n)=hammingweight(n-1)%2==0 && hammingweight(n+1)%2==0 && isprime(n) \\ Charles R Greathouse IV, Oct 09 2013 CROSSREFS Subsequence of A002145. Cf. A000069, A001969, A007814, A027697, A092246, A095282. Seems to consist of all primes in A233388. Sequence in context: A201719 A107201 A189888 * A224383 A139829 A138355 Adjacent sequences: A227927 A227928 A227929 * A227931 A227932 A227933 KEYWORD nonn,base,easy AUTHOR Juri-Stepan Gerasimov, Oct 06 2013 EXTENSIONS Entries checked by R. J. Mathar, Oct 08 2013 STATUS approved

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Last modified September 12 12:03 EDT 2024. Contains 375851 sequences. (Running on oeis4.)