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A277577 a(n) is the number of primes of the form (6n+3) +/- 3^k +/- 1, 1<=k<(t-2) and t is the number of digits of (6n+3)'s balanced ternary representation. 1
4, 7, 7, 6, 6, 6, 9, 8, 8, 8, 9, 8, 8, 7, 6, 9, 8, 8, 5, 8, 9, 8, 10, 9, 10, 9, 9, 9, 8, 10, 11, 8, 10, 7, 6, 8, 8, 11, 9, 7, 8, 9, 8, 10, 9, 10, 8, 7, 5, 8, 10, 6, 10, 5, 5, 10, 7, 9, 9, 9, 8, 12, 10, 8, 11, 10, 9, 10, 10, 9, 11, 11, 12, 8, 8, 11, 10, 9, 9, 10, 10, 10, 8, 7, 12, 10, 8, 8, 8, 7, 9, 6, 9, 11, 10, 11, 8, 11, 10, 11, 9, 10, 10, 9, 8, 10, 11, 11, 8, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first a few of a(n)=0 terms of this sequence appear on n=72030, 228439, 282059, 383424, 384204, 593477, 710787, 736541, 1057465, 1628226, 1831745, 1892512, 1922647, 2128995, 2244660, 2260650, 2276272, 2289706, 2374644, 2507484, 2633477, 2681747, 2695747, 2875824, 2889472, 2913659 up to n<=3000000.

LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000

EXAMPLE

n=1: 6n+3=9. 9=(100)_bt. 1<=k<=(3-2)=1. When k=1, (6n+3)+/-3^1+/-1 = 5, 7, 11, 13, all primes. So a(1) = 4;

n=2: 6n+3=15. 15=(1TT0)_bt. 1<=k<=(4-2)=2. When k=1, (6n+3)+/-3^1+/-1 = 11, 13, 17, 19, all primes; when k=2, (6n+3)+/-3^2+/-1 = 5, 7, 23, 25, three primes.  Totals 7. So a(2) = 7.

MATHEMATICA

BTDigits[m_Integer, g_] :=

  Module[{n = m, d, sign, t = g},

   If[n != 0, If[n > 0, sign = 1, sign = -1; n = -n];

    d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++];

    While[Length[t] < d, PrependTo[t, 0]];

    t[[Length[t] + 1 - d]] = sign;

    t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];

Table[trib = 6*n + 3; t = BTDigits[trib, {}]; l = Length[t]; ct = 0;

Do[If[PrimeQ[trib - 3^j - 1], ct++];

  If[PrimeQ[trib - 3^j + 1], ct++]; If[PrimeQ[trib + 3^j + 1], ct++];

  If[PrimeQ[trib + 3^j - 1], ct++], {j, 1, l - 2}]; ct, {n, 1, 111}]

CROSSREFS

Cf. A196698.

Sequence in context: A201940 A075113 A197739 * A011222 A157298 A070326

Adjacent sequences:  A277574 A277575 A277576 * A277578 A277579 A277580

KEYWORD

nonn,base

AUTHOR

Lei Zhou, Oct 20 2016

STATUS

approved

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Last modified September 24 05:29 EDT 2021. Contains 347623 sequences. (Running on oeis4.)