A329336 -id:A329336 - cp's OEIS frontend

A328906 Decimal expansion of the solution x = 0.4895363211996... to 1 + 2^x = 6^x.

4, 8, 9, 5, 3, 6, 3, 2, 1, 1, 9, 9, 6, 4, 9, 4, 8, 8, 6, 8, 9, 8, 7, 5, 3, 1, 6, 8, 2, 2, 6, 5, 0, 1, 8, 9, 4, 0, 3, 5, 8, 6, 5, 1, 5, 7, 7, 1, 9, 1, 2, 1, 2, 7, 8, 4, 6, 4, 3, 6, 6, 7, 8, 6, 1, 9, 2, 5, 5, 6, 2, 8, 2, 5, 5, 8, 6, 6, 8, 4, 4, 8, 2, 3, 5, 0, 9, 7, 2, 4, 0, 4, 3, 3, 9, 0, 0, 5, 0

Offset: 0

M. F. Hasler, Nov 11 2019

			0.489536321199649488689875316822650189403586515771912127846436678619255628...

Cf. A329336 (continued fraction).

Cf. A242208 (1 + 2^x = 4^x), A328900 (2^x + 3^x = 4^x), A328904 (1 + 3^x = 5^x), A328905 (1 + 2^x = 5^x), A328907 (1 + 3^x = 6^x).

RealDigits[x /. FindRoot[1 + 2^x == 6^x, {x, 1}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Jun 28 2023 *)

print(c=solve(x=0,1, 1+2^x-6^x)); digits(c\.1^default(realprecision))[^-1] \\ [^-1] to discard possibly incorrect last digit. Use e.g. \p999 to get more digits. - M. F. Hasler, Oct 31 2019

A329920 Smallest k such that 6kA121940(n)-1 and 6kA121940(n)+1 are twin primes.

Original entry on oeis.org

1, 2, 2, 15, 36, 10, 13, 26, 30, 228, 24, 138, 520, 59, 110, 456, 700, 670, 146, 300, 390, 53, 2335, 340, 159, 340, 65, 475, 785, 1145, 759, 3557, 490, 169, 990, 1527, 704, 3379, 1426, 1927, 2397, 600, 1603, 4809, 9815, 58, 35, 364, 361, 123, 2197, 4054, 1867, 1827, 5048

Offset: 1

Pierre CAMI, Nov 24 2019

nonn

			A121940(1)=7, 6*1*7-1=41, 41 and 43 are twin primes so a(1)=1.
A121940(2)=91, 6*2*91-1=1091, 1091 and 1093 are twin primes so a(2)=2.

Cf. A001359, A002476, A006512, A121940, A173937, A329336, A329916.

lista(nn) = {my(pp = 1); forprime (p = 1, nn, if (Mod(p, 6) == +1, pp *= p; my(k=1); while (!isprime(6*k*pp-1) || !isprime(6*k*pp+1), k++); print1(k, ", ");););} \\ Michel Marcus, Nov 25 2019

cp's OEIS Frontend

A328906 Decimal expansion of the solution x = 0.4895363211996... to 1 + 2^x = 6^x.

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A329920 Smallest k such that 6kA121940(n)-1 and 6kA121940(n)+1 are twin primes.

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PARI

cp's OEIS Frontend

A328906 Decimal expansion of the solution x = 0.4895363211996... to 1 + 2^x = 6^x.

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PARI

A329920 Smallest k such that 6*k*A121940(n)-1 and 6*k*A121940(n)+1 are twin primes.

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PARI

A329920 Smallest k such that 6kA121940(n)-1 and 6kA121940(n)+1 are twin primes.