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A292425 The smallest positive number of the form 3^n-2^a-2^b. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

PROG

(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<<logint(t, 2); t-=1<<logint(t, 2); t} \\ Andrew Howroyd, Dec 23 2019

CROSSREFS

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

Sequence in context: A010292 A133104 A322730 * A095988 A189898 A082525

Adjacent sequences:  A292422 A292423 A292424 * A292426 A292427 A292428

KEYWORD

nonn

AUTHOR

Tomohiro Yamada, Sep 29 2017

EXTENSIONS

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

STATUS

approved

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Last modified September 21 04:58 EDT 2020. Contains 337267 sequences. (Running on oeis4.)