A221129 -id:A221129 - cp's OEIS frontend

3, 10, 35, 132, 517, 2054, 8199, 32776, 131081, 524298, 2097163, 8388620, 33554445, 134217742, 536870927, 2147483664, 8589934609, 34359738386, 137438953491, 549755813908, 2199023255573, 8796093022230, 35184372088855, 140737488355352, 562949953421337

Offset: 1

Jaroslav Krizek, Jan 02 2013

nonn

Conjecture: a(n ) = the smallest numbers w such that numbers w, w+1,…, w+k-1 for k=1,2,…n are numbers of form h*2^m + m, where 1<=h <2^m, m = natural number (see A221129).
a(5) = 517 because numbers 517, 518, 519, 520, 521 are numbers of presented form.
517 = 16*2^5 + 5, 518 = 8*2^6 + 6, 519 = 4*2^7 + 7, 520 = 2*2^8 + 8, 521 = 1*2^9 + 9 (that is, numbers (2^(n-k))*(2^(n+k-1))+n+k-1, for k=1,2,,...n).

			a(5)=2^(2*5-1)+5=517.

Jaroslav Krizek, Table of n, a(n) for n = 1..53
Index entries for linear recurrences with constant coefficients, signature (6,-9,4)

Cf. A221129, A199116.

a(n+1) = a(n) + 3*2^(2*n-1)+1 = a(n) + 6*4^(n-1)+1 = a(n) + 2^(2*n+1) - 2^(2*n-1) + 1 = a(n) + A199116(n-1).

G.f. -x*(3-8*x+2*x^2) / ( (4*x-1)*(x-1)^2 ). - R. J. Mathar, Jan 17 2013

cp's OEIS Frontend

A221130 a(n) = 2^(2*n - 1) + n.

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