A130206 Primes in lunar arithmetic in base 3 written in base 10.

5, 6, 7, 8, 11, 19, 20, 23, 29, 32, 34, 35, 38, 46, 47, 55, 56, 58, 59, 61, 62, 64, 65, 68, 71, 73, 74, 77, 83, 86, 88, 89, 95, 97, 98, 103, 104, 106, 107, 110, 119, 127, 128, 136, 137, 142, 143, 145, 146, 154, 155, 163, 164, 166, 167, 169, 170, 173, 175, 176, 178, 179, 184, 185, 187, 188, 190

Offset

1,1

Links

Table of n, a(n) for n=1..67.

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

Index entries for sequences related to dismal (or lunar) arithmetic

Prog

(Python)
def ternary(m):
    if m == 0: return '0'
    s = []
    while m:
        m, r = divmod(m, 3)
        s.append(str(r))
    return ''.join(reversed(s))
def addn(m1, m2):
    s1, s2 = ternary(m1), ternary(m2)
    len_max = max(len(s1), len(s2))
    return int(''.join(max(i, j) for i, j in zip(s1.rjust(len_max, '0'), s2.rjust(len_max, '0'))))
def muln(m1, m2):
    s1, s2, prod =  ternary(m1), ternary(m2), '0'
    for i in range(len(s2)):
        k = s2[-i-1]
        prod = addn(int(str(prod), 3), int(''.join(min(j, k) for j in s1), 3)*3**i)
    return prod
for m in range(3, 201):
    i, ct = 1, 0
    for i in range(1, m+1):
        if i == 2: continue
        j = i
        for j in range(1, m+1):
            if j == 2: continue
            ij = int(str(muln(i, j)), 3)
            if ij == m: ct += 1; break
        if ct > 0: break
if ct == 0: print(m) # Ya-Ping Lu, Dec 30 2020

Crossrefs

Cf. A170806.

Sequence in context: A200259 A339746 A262513 * A178502 A047322 A236242

Adjacent sequences: A130203 A130204 A130205 * A130207 A130208 A130209

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 30 2010

Extensions

Entries >=83 from R. J. Mathar, Nov 23 2015

Status

approved