cp's OEIS Frontend

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).

%I A387414 #26 Sep 01 2025 23:43:29
%S A387414 1,4,10,18,57,348,1054,2626,60625,68727,129260,192276,675348,960320,
%T A387414 5368464,12371554,30078308,356311953,1158654378,1673018314
%N 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).
%C A387414 Numbers k such that A003961(k) = 2^e * k + r, for some k >= 1, e >= 0, 0 <= r < 2^e.
%H A387414 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A387414 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%e A387414 A007088(4) = 100, and A007088(A003961(4)) = A007088(9) = 1001 begins with the same binary string, therefore 4 is included.
%e A387414 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.
%o A387414 (PARI)
%o A387414 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A387414 is_A387414(n) = { my(s=A003961(n)); while(s>n, s >>= 1); (s==n); };
%Y A387414 Positions of 0's in A387413.
%Y A387414 Cf. A000523, A003961, A007088, A387412.
%Y A387414 Subsequences: A348514 (which is also a subsequence of A387411).
%K A387414 nonn,more,new
%O A387414 1,2
%A A387414 _Antti Karttunen_, Sep 01 2025