A054047 -id:A054047 - cp's OEIS frontend

A045574 Numbers that are still numbers when turned upside down (uses only digits 0, 1, 6, 8, 9 with no final 0's).

0, 1, 6, 8, 9, 11, 16, 18, 19, 61, 66, 68, 69, 81, 86, 88, 89, 91, 96, 98, 99, 101, 106, 108, 109, 111, 116, 118, 119, 161, 166, 168, 169, 181, 186, 188, 189, 191, 196, 198, 199, 601, 606, 608, 609, 611, 616, 618, 619, 661, 666, 668, 669, 681, 686, 688, 689, 691, 696, 698, 699

Offset: 1

Erich Friedman

"No final 0's" means that the rotated number should not have leading zeros; the single digit of the number 0 itself is not considered as such.

Michel Marcus, Table of n, a(n) for n = 1..2501
Index entries for sequences related to final digits of numbers

Cf. A000787, A018847, A054047, A057770.

is_A045574(n)=n%10 & !setminus(Set(Vec(Str(n))),Vec("01689")) || !n  \\ M. F. Hasler, May 04 2012

More terms from Michel Marcus, Dec 27 2020

A080789 Numbers that are primes when turned upside down.

Original entry on oeis.org

11, 19, 61, 68, 101, 109, 110, 116, 118, 161, 166, 169, 181, 188, 190, 199, 601, 608, 610, 616, 619, 661, 680, 1006, 1010, 1018, 1019, 1061, 1066, 1081, 1090, 1091, 1096, 1100, 1106, 1108, 1109, 1118, 1160, 1169, 1180, 1181, 1186, 1601, 1606, 1609, 1610, 1618

Offset: 1

P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 12 2003

P. Giannopoulos, The Brainteasers (unpublished)

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A057770, A054047, A080788.

from sympy import isprime
from itertools import product
def ud(s):
    return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def auptod(maxdigits):
    alst = []
    for d in range(1, maxdigits+1):
        for start in "16":
            for p in product("01689", repeat=d-1):
                s = start + "".join(p)
                t, udt = int(s), int(ud(s))
                if isprime(udt): alst.append(t)
    return alst
print(auptod(4)) # Michael S. Branicky, Nov 19 2021

610 inserted and a(24) and beyond from Michael S. Branicky, Nov 19 2021

A054044 Grundy function for turn-at-most-7-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 127, 128, 256, 512, 911, 1024, 1459, 1749, 1897, 2048, 2518, 2787, 2874, 3320, 3357, 3662, 4004, 4096, 8192, 16384, 28687, 32768, 45107, 53333, 57449, 65536, 77910, 86115, 90170, 102520, 106525, 114766, 127012

Offset: 1

N. J. A. Sloane, Apr 29 2000

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 433.

Cf. A000069, A033623, A054016, A054047, etc.

A054045 Grundy function for turn-at-most-8-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 255, 256, 512, 1024, 2048, 3855, 4096, 8192, 13107, 16384, 21845, 27306, 32768, 38506, 65536, 71576, 92115, 101470, 131072, 138406, 172589, 240014, 262144, 272069, 380556, 524288, 536169, 679601

Offset: 1

N. J. A. Sloane, Apr 29 2000

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 433.

Jingzhe Tang, Table of n, a(n) for n = 1..64

Cf. A000069, A033623, A054016, A054047, etc.

A054046 Grundy function for turn-at-most-9-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 512, 1024, 2048, 4096, 7711, 8192, 16384, 26215, 32768, 43691, 54613, 65536, 77013, 131072, 143153, 184230, 202940, 262144, 276813, 345179, 480029, 524288, 544139, 761113, 1048576, 1072338

Offset: 1

N. J. A. Sloane, Apr 29 2000

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 433.

Cf. A000069, A033623, A054016, A054047, etc.

A208646 Calendar Problem #27, April 2012 Mathematics Teacher.

Original entry on oeis.org

9861, -1986, 9681, -1896, 8961, -1968, 8691, -1698

Offset: 1

Jonathan Vos Post, Mar 01 2012

The numbers are paired on the basis of rotational symmetry with alternating signs.

			If you rotate the first number, 9861, 180 degrees about its center, and put a negative sign in front, you get the second number: -1986. Similarly, the third and fourth numbers are rotations of each other, as well as of the fifth and sixth numbers.  Therefore the eighth number is the rotation and negation of the seventh number, 8961, which would be -1698.

Margaret Coffey, Editor, Calendar Problem #27, April 2012 Mathematics Teacher, pp. 521, 524.

Cf. A045574, A054047.

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A045574 Numbers that are still numbers when turned upside down (uses only digits 0, 1, 6, 8, 9 with no final 0's).

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A080789 Numbers that are primes when turned upside down.

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A054044 Grundy function for turn-at-most-7-coins game.

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A054045 Grundy function for turn-at-most-8-coins game.

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A054046 Grundy function for turn-at-most-9-coins game.

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A208646 Calendar Problem #27, April 2012 Mathematics Teacher.

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