A387414 Numbers k such that the binary expansion of k is a prefix of the binary expansion of A003961(k), where A003961 is fully multiplicative with a(p) = nextprime(p).

1, 4, 10, 18, 57, 348, 1054, 2626, 60625, 68727, 129260, 192276, 675348, 960320, 5368464, 12371554, 30078308, 356311953, 1158654378, 1673018314

Offset

1,2

Comments

Numbers k such that A003961(k) = 2^e * k + r, for some k >= 1, e >= 0, 0 <= r < 2^e.

Links

Table of n, a(n) for n=1..20.

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to prime indices in the factorization of n.

Example

A007088(4) = 100, and A007088(A003961(4)) = A007088(9) = 1001 begins with the same binary string, therefore 4 is included.
A007088(18) = 10010, and A007088(A003961(18)) = A007088(75) = 1001011 begins with the same binary string, therefore 18 is included as a term. Also, 75 = 2^2 * 18 + 3.

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
is_A387414(n) = { my(s=A003961(n)); while(s>n, s >>= 1); (s==n); };

Crossrefs

Positions of 0's in A387413.

Cf. A000523, A003961, A007088, A387412.

Subsequences: A348514 (which is also a subsequence of A387411).

Sequence in context: A063591 A009912 A318070 * A073262 A353189 A362100

Adjacent sequences: A387411 A387412 A387413 * A387415 A387416 A387417

Keyword

nonn,more

Author

Antti Karttunen, Sep 01 2025

Status

approved