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A281424 Numbers k such that 16*(10^k - 1)/3 + 1 is prime. 0
6, 23, 65, 82, 108, 188, 300, 342, 401, 584, 1570 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All prime numbers of the form 16*(10^k - 1)/3 + 1 are terms of A002476.

For any k = a(n), the m-index of 16*(10^k - 1)/3 + 1 in sequence 6m+1 contains exactly a(n) digits, and each digit is 8. E.g., while k = a(1) = 6, 16*(10^6 - 1)/3 + 1 = 6*888888 + 1 = 5333329.

In any number of form 16*(10^k - 1)/3 + 1, its first digit is 5, its two last digits are 29, and each other digit that is between (5...29) is 3.

For k=1, k=2, k=3, the numbers of form 16*(10^k - 1)/3 + 1 are squares of the primes 7, 23, and 73, respectively (see A001248).

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

For k = a(1) = 6, 16*(10^6 - 1)/3 + 1 = 5333329 and 16*(10^6 - 1)/3 + 1 is prime.

MATHEMATICA

Select[Range@ 3000, PrimeQ[16 (10^# - 1)/3 + 1] &] (* Michael De Vlieger, Jan 23 2017 *)

CROSSREFS

Cf. A002476.

Sequence in context: A208598 A119712 A273314 * A005745 A213557 A273386

Adjacent sequences:  A281421 A281422 A281423 * A281425 A281426 A281427

KEYWORD

nonn,more

AUTHOR

Sergey Pavlov, Jan 21 2017

STATUS

approved

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Last modified December 12 01:08 EST 2017. Contains 295936 sequences.