This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
{l=0;r=0; forprime( p=1, default(primelimit), if( bittest( norml2(binary(p)),0), l>r & print1(r=l ", "); l & l=0, l++))} \\ M. F. Hasler, Dec 12 2010
2 is a prime and A001969(2) = 3, a prime also, thus 2 is in this sequence; 3 is a prime and A001969(3) = 5, a prime also, thus 3 is in this sequence; 139 is a prime A001969(139) = 277, a prime also, thus 139 is this sequence.
is(n)=isprime(n) && isprime(2*n--+hammingweight(n)%2) \\ Charles R Greathouse IV, Jan 02 2014
isevil:= proc(n) convert(convert(n,base,2),`+`)::even end proc:
N:= 1000: # for terms <= N
V:= Vector(N,1):
for i from 1 to N do
if isevil(i) then V[[seq(j,j=2*i .. N, i)]]:= 0
else V[i]:= 0
fi
od:
select(t -> V[t]=1, [$1..N]); # Robert Israel, Jun 18 2025
evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; q[n_] := evilQ[n] && AllTrue[Divisors[n], # == n || ! evilQ[#] &]; Select[Range[600], q] (* Amiram Eldar, May 31 2025 *)
isevil(n) = hammingweight(n) % 2 == 0;
noevildiv(n) = {fordiv(n, d, if ((d < n) && isevil(d), return (0)); ); 1; }
isok(n) = isevil(n) && noevildiv(n); \\ Michel Marcus, May 31 2025
a(6) = 27 is a term because 3, 9 and 27 are all evil. The first term that is a fourth power is 277^4 = 5887339441. The first term that is a fifth power is 317^5 = 3201078401357.
isevil:= proc(n) convert(convert(n,base,2),`+`)::even end proc:
M:= 1000: # for terms <= M
R:= NULL:
p:= 1:
do
p:= nextprime(p);
if p > M then break fi;
for k from 1 do
z:= p^k;
if z > M then break fi;
if isevil(z) then R:= R, z
else break
fi
od
od:
sort([R]);
23 is in this sequence because A000120(3*23-1) = A000120(68) = 2 (even number). 29 is in this sequence because A000120(3*29-1) = A000120(86) = 4 (even number).
Select[Prime@Range@200, EvenQ@ First@ DigitCount[3#-1, 2] &] (* Giovanni Resta, Jan 26 2014 *)
isok(p) = isprime(p) && !(hammingweight(3*p-1) % 2); \\ Michel Marcus, Jan 18 2014
aQ[n_] := EvenQ @ Total @ Rest @ Reverse @ Mod[NestWhileList[(# - Mod[#, 2])/-2 &, n, # != 0 &], 2]; s = {}; p = 2; c = 0; Do[If[aQ[p], c++, c--]; If[c == 0, AppendTo[s, p]]; p = NextPrime[p], {10^3}]; s (* Amiram Eldar, Sep 22 2019 after Michael De Vlieger at A268272 *)
a(1) = 2, because c1(2) = 1 and c2(2) = 0, so abs(c1(2) - c2(2)) = 1 >= 1, and no lesser prime satisfies this.
{ r = 0; n = 1; forprime (p = 2, 1787, r += (-1)^hammingweight(p); if (n==abs(r), print1 (p", "); n++;);); } \\ Rémy Sigrist, Mar 01 2023
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