A248140 -id:A248140 - cp's OEIS frontend

A248138 Consider the partition of consecutive evil numbers (A001969) into minimal blocks such that concatenation of numbers in each block is an odious number (A000069). Sequence lists numbers of evil numbers in each block.

3, 2, 2, 3, 2, 3, 4, 2, 2, 5, 2, 5, 3, 2, 2, 2, 2, 2, 6, 4, 3, 6, 4, 7, 4, 5, 3, 4, 3, 2, 3, 3, 4, 2, 2, 2, 2, 2, 2, 2, 4, 3, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 3, 5, 2, 3, 3, 6, 2, 4, 5, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 4, 3, 2, 2, 2, 3

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, Oct 02 2014

nonn

The blocks of consecutive evil numbers of the partition are

0,3,5| 6,9| 10,12| 15,17,18| 20,23| 24,27,29| 30,33,34,36| 39,40| 43,45| 46,48,51,53,54| 57,58| 60,63,65,66,68|, etc.

Cf. A000069, A001969, A248140, A248145, A248146.

A248009 Partition of the positive odd integers into minimal blocks such that the concatenation of the numbers in each block is an evil number (A001969). Sequence lists the evil numbers obtained in this way.

Original entry on oeis.org

135, 7911, 131517, 19212325272931, 33, 35373941, 43, 45, 4749, 51, 53, 5557, 596163, 65, 676971, 737577, 798183, 85, 8789, 9193, 95, 9799101103105, 107109, 111, 113, 115117119, 121123125127129, 131133, 135, 137139, 141, 143145147, 149, 151153155157, 159

Offset: 1

Vladimir Shevelev, Oct 05 2014

The numbers of the consecutive positive odd integers in the blocks of the partition are 3,3,3,7,1,4,1,1,2,1,1,2,3,1,3,3,3,1,2,2,...

			a(1)=135, since 1 and 13 are odious numbers, while 135 is evil.

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Cf. A248138, A248140, A248145, A248146, A248171, A248172.

lista(nn) = {s = ""; forstep(n=1, nn, 2, ns = concat(s, Str(n)); if ((hammingweight(eval(ns)) % 2) == 0, print1(ns, ", "); s = "", s = ns););} \\ Michel Marcus, Oct 09 2014

More terms from Peter J. C. Moses, Oct 09 2014

A248171 Partition of the positive integers on minimal blocks such that concatenation of numbers in each block is an evil number (A001969). Sequence lists the evil numbers obtained in this way.

Original entry on oeis.org

12, 3, 45, 6, 78, 9, 10, 1112, 1314, 15, 161718, 1920, 2122, 23, 24, 2526, 27, 2829, 30, 3132, 33, 34, 3536, 37383940, 414243, 4445464748, 495051, 52535455, 5657, 58, 5960, 6162, 63, 646566, 6768, 6970, 71, 72, 7374, 75, 7677787980, 818283, 8485868788, 89, 90

Offset: 1

Vladimir Shevelev, Oct 03 2014

The numbers of the consecutive positive integers over blocks of the partition are 2,1,2,1,2,1,1,2,2,1,3,2,2,1,1,2,1,...

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Cf. A000069 (odious), A001969 (evil), A248009, A248138, A248140, A248172 (similar, with odious).

from itertools import count
def evil(n): return bin(n)[2:].count('1') % 2 == 0
def aupton(terms):
    alst, t = [], 0
    for k in count(1):
        t = int(str(t) + str(k))
        if evil(t):
            alst.append(t)
            t = 0
            if len(alst) >= terms: return alst
print(aupton(45)) # Michael S. Branicky, Dec 03 2021

More terms from Peter J. C. Moses, Oct 04 2014

A248172 Partition of the positive integers on minimal blocks such that concatenation of numbers in each block is an odious number (A000069). Sequence lists the odious numbers obtained in this way.

Original entry on oeis.org

1, 2, 345, 67, 8, 9101112, 13, 14, 1516, 1718, 19, 202122232425, 26, 2728, 2930, 31, 32, 3334, 35, 3637, 38, 3940, 41, 42, 4344454647, 4849, 50, 5152, 5354, 55, 56, 5758, 59, 6061, 62, 6364, 6566, 67, 686970, 7172737475, 76, 7778, 79, 808182, 8384, 8586, 87

Offset: 1

Vladimir Shevelev, Oct 03 2014

The numbers of the consecutive positive integers over blocks of the partition are 1,1,3,2,1,4,1,1,2,2,1,6,1,2,2,1,1,2,1,...

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Cf. A000069 (odious), A001969 (evil), A248009, A248138, A248140, A248171 (similar, with evil).

More terms from Peter J. C. Moses, Oct 04 2014

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A248138 Consider the partition of consecutive evil numbers (A001969) into minimal blocks such that concatenation of numbers in each block is an odious number (A000069). Sequence lists numbers of evil numbers in each block.

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A248009 Partition of the positive odd integers into minimal blocks such that the concatenation of the numbers in each block is an evil number (A001969). Sequence lists the evil numbers obtained in this way.

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A248171 Partition of the positive integers on minimal blocks such that concatenation of numbers in each block is an evil number (A001969). Sequence lists the evil numbers obtained in this way.

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A248172 Partition of the positive integers on minimal blocks such that concatenation of numbers in each block is an odious number (A000069). Sequence lists the odious numbers obtained in this way.

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