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A208982 Numbers n such that the next larger number with mutual Hamming distance 1 is prime. 4
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 16, 17, 18, 19, 21, 22, 23, 27, 28, 29, 30, 36, 39, 40, 41, 42, 43, 45, 46, 52, 57, 58, 60, 63, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 81, 82, 88, 95, 96, 99, 100, 101, 102, 105, 106, 108, 111, 112, 119, 123, 125, 126, 129, 130, 136, 137, 138, 147, 148, 149, 150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If p is prime, then p-1 is in the sequence.

Using the prime number theorem in arithmetic progressions k*n+b with gcd(k,b)=1 and its uniformity over k<=exp(c*sqrt(log(x))), one can prove that the counting function of a(n)<=x is equivalent to 2*x/log(x), as x tends to infinity.

LINKS

Table of n, a(n) for n=1..71.

PROG

(PARI) isok(n) = my(nextn = n+1); while (hammingweight(bitxor(n, nextn)) != 1, nextn++); isprime(nextn); \\ Michel Marcus, Jul 01 2014

CROSSREFS

Cf. A205509, A205510, A205511, A205302, A205649, A205533, A122565, A206852, A206853, A206960, A209085.

Sequence in context: A117073 A063952 A277025 * A018710 A018509 A134950

Adjacent sequences:  A208979 A208980 A208981 * A208983 A208984 A208985

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Mar 04 2012

STATUS

approved

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Last modified December 15 12:13 EST 2019. Contains 329999 sequences. (Running on oeis4.)