A342704 Characteristic function of base-2 lunar primes: a(n) = 1 if n is a base-2 lunar prime, otherwise 0.

0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1

Offset

1

Links

Table of n, a(n) for n=1..87.

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011.

Index entries for characteristic functions

Index entries for sequences related to binary expansion of n

Example

a(9) = 1 because 9 does not occur anywhere in the inner portion of the OR-numbral multiplication table A067138 (apart from its row/column 1). On the other hand, a(7) = 0 because A067138(3,3) = 7. - Antti Karttunen, Mar 21 2021

Prog

(Python)
def addn(m1, m2):
    s1, s2 = bin(m1)[2:].zfill(0), bin(m2)[2:].zfill(0)
    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 = bin(m1)[2:].zfill(0), bin(m2)[2:].zfill(0), '0'
    for i in range(len(s2)):
        k = s2[-i-1]; prod = addn(int(str(prod), 2), int(''.join(min(j, k) for j in s1), 2)*2**i)
    return prod
m = 1; m_size = 7; L_im = [1]
while m <= 2**m_size:
    for i in range(2, m + 1):
        im_st = str(muln(i, m)); im = int(im_st, 2); im_len = len(im_st)
        if im_len > m_size: break
        if im not in L_im: L_im.append(im)
    print(1) if m not in L_im else print(0); m += 1

Crossrefs

Characteristic function of A067139.

Cf. A342678 (partial sums), A067138, A169912, A171000, A171750, A171752.

Cf. also A010051, A091225.

Sequence in context: A209229 A365089 A295890 * A284622 A379184 A215581

Adjacent sequences: A342701 A342702 A342703 * A342705 A342706 A342707

Keyword

nonn,base

Author

Ya-Ping Lu, Mar 19 2021

Status

approved