A065084 Smallest prime having alternating bit sum (A065359) equal to n.

3, 7, 5, 0, 277, 1109, 0, 17749, 70997, 0, 1398037, 5526869, 0, 72701269, 357915989, 0, 5659514197, 22902297941, 0, 297784399189, 1465948394837, 0, 23456248042837, 89426945725781, 0, 1430831131612501, 6004798429418837, 0

Offset

0,1

Comments

Only 3d = 11b has an alternating sum of 0 and alternated sums of 3*k are impossible for primes.

Links

Washington Bomfim, Table of n, a(n) for n = 0..121

Example

a(4)=277 since the smallest number having alternating bit sum n is (4^n-1)/3, which for n = 4 is 85. Because 85 =(1010101)2 is composite, the next number with alternating bit sum 4 is the prime (100010101)2 = 277. - Washington Bomfim, Jan 21 2011

Mathematica

f[n_] := (d = Reverse[ IntegerDigits[n, 2]]; l = Length[d]; s = 0; k = 1; While[k < l + 1, s = s - (-1)^k*d[[k]]; k++ ]; s); a = Table[ f[ Prime[n]], {n, 1, 10^6} ]; b = Table[0, {13} ];
Do[ If[ a[[n]] > -1 && b[[a[[n]] + 1]] == 0, b[[a[[n]] + 1]] = Prime[n]], {n, 1, 10^6} ]; b

Prog

(PARI)M(n)={return((4^n - 1)/3 + 2^(2*n) - 2^(2*n-2))};
T(n, k)={pow2=2^(2*n-2); k+=pow2; for(j=1, n-2, pow2/=4; k-=pow2; if(isprime(k), return(k), k+=pow2; )); return(k)};
T2(n, k)={pow2=2; for(j=1, n, k+=pow2; if(isprime(k), return(k), k-=pow2; pow2*=4)); return(k)};
print("0 3"); print("1 7"); print("2 5"); print("3 0"); for(n=4, 127, if(n%3==0, print(n, " 0"), k=M(n); if(isprime(k), print(n, " ", k), k=T(n, k); if(isprime(k), print(n, " ", k), k=T2(n, k); if(isprime(k), print(n, " ", k), print("a(", n, ") not found")))))) \\ Washington Bomfim, Jan 22 2011

Crossrefs

Cf. A065359, A002450, A065085.

Sequence in context: A086242 A322931 A096627 * A338769 A132742 A267317

Adjacent sequences: A065081 A065082 A065083 * A065085 A065086 A065087

Keyword

base,nonn

Author

Robert G. Wilson v, Nov 09 2001

Extensions

a(14)-a(27) from Washington Bomfim, Jan 21 2011

Status

approved