A292425 The smallest positive number of the form 3^n-2^a-2^b.

0, 0, 3, 1, 51, 89, 11, 417, 1251, 9897, 13307, 3057, 21459, 64377, 1765995, 1103681, 28476867, 51876169, 21410779, 265558929, 796676787, 5611255833, 8243832907, 3256662241, 22654888611, 67964665833, 1028527718331, 886559899441, 15853819231635, 29969271650489

Offset: 1

Author

Tomohiro Yamada, Sep 29 2017

Keywords

• nonn

Comments

It follows from a work of Vojta that a(n) tends to infinity as n tends to infinity.

References

• P. Vojta, Integral points on varieties. Thesis, Harvard, 1983.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Mo Deze and R. Tijdeman, Exponential diophantine equations with four terms, Indag. Math. N.S. 3 (1992), 47--57.
• R. Tijdeman and Lian Xiang Wang, Sums of products of powers of given prime numbers, Pacific J. Math. 132, (1988), 177--193.
• Tomohiro Yamada, On the diophantine equation x^m=y^n1+y^n2+...+y^nk, Glasgow Math. J. 51 (2009), 143--148.

Crossrefs

Cf. A056577 (smallest 3^n-2^k).

Programs

PARI

f(x)=x-2^floor(log(x)/log(2)); g(x)=f(f(x)); a(n)=g(3^n)

PARI

a(n)={my(t=3^n); t-=1<Andrew Howroyd, Dec 23 2019

Extensions

Terms a(15) and beyond from Andrew Howroyd, Dec 23 2019