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A342704 Characteristic function of base-2 lunar primes: a(n) = 1 if n is a base-2 lunar prime, otherwise 0. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A029691 A209229 A295890 * A284622 A215581 A156595

Adjacent sequences:  A342701 A342702 A342703 * A342705 A342706 A342708

KEYWORD

nonn,base

AUTHOR

Ya-Ping Lu, Mar 19 2021

STATUS

approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)