A376298 Numbers which are the sum of at least three successive terms of a geometric progression.

7, 13, 14, 15, 21, 26, 28, 30, 31, 35, 39, 40, 42, 43, 45, 49, 52, 56, 57, 60, 62, 63, 65, 70, 73, 75, 77, 78, 80, 84, 85, 86, 90, 91, 93, 98, 104, 105, 111, 112, 114, 117, 119, 120, 121, 124, 126, 127, 129, 130, 133, 135, 140, 143, 146, 147, 150, 154, 155, 156, 157

Offset: 1

Author

Andrew Howroyd, Sep 19 2024

Keywords

• nonn

Comments

Multiples of terms in A053696.

Numbers of the form m*(b^n-1)/(b-1) for n > 2 and b > 1, m > 0.

Examples

			7 is a term because 7 = 1 + 2 + 4.
13 is a term because 13 = 1 + 3 + 9.
14 is a term because 14 = 2 + 4 + 8.
15 is a term because 15 = 1 + 2 + 4 + 8.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000
• Wikipedia, Geometric progression.

Crossrefs

Cf. A053696, A084733, A085104.

Programs

PARI

B(k,lim)={vector(logint(lim*(k-1)+1,k)-2, i, (k^(i+2) - 1)/(k-1))}
upto(lim=200)={my(v=concat(vector(sqrtint(lim)-1, k, B(k+1,lim)))); Set(concat(vector(#v, i, my(t=v[i]); t*[1..lim\t])))}