A033147 -id:A033147 - cp's OEIS frontend

A383322 Lexicographically earliest sequence of distinct terms such that replacing each term k with k! does not change the succession of digits.

1, 2, 198, 15, 5, 24, 3, 0, 56, 4, 800, 260, 18, 181, 7, 120, 43, 26, 25, 78, 46, 6, 11, 45, 67, 2580, 8, 37, 34, 49, 61, 66, 465, 63, 9, 28, 62, 93, 960, 65, 410, 626, 13, 82, 98, 59, 32, 659, 453, 242, 255, 580, 939, 42, 70, 44, 932, 22, 55, 38, 389, 50

Offset: 1

Dominic McCarty, Apr 23 2025

Similarly to A302656, this sequence contains very large jumps. For example, a(131) = 4*10^47, a(702) = 496*10^199, a(2808) = 5712*10^643, etc.

			Let b(n) = a(n)!
(a(n)): 1, 2, 198, 15, 5, 24, 3, 0, 56, 4, 800, 260, 18, ...
(b(n)): 1, 2, 198155243056480026018[...] (350 digits omitted), ...

Dominic McCarty, Table of n, a(n) for n = 1..10000
Dominic McCarty, Table of n, a(n)! for n = 1..100

Cf. A033147, A383318, A383320, A302656.

from sympy import factorial
from itertools import count
a, sa, sb = [1, 2, 198], "12198", "12"+str(factorial(198))
for _ in range(20):
    a.append(next(n for k in count(1) if not (n := int(sb[len(sa):len(sa)+k])) in a and (0 not in a or not (len(sb) > len(sa) + k and sb[len(sa) + k] == "0"))))
    sa += str(a[-1]); sb += str(factorial(a[-1]))
print(a)

A229629 Numbers k such that k is in the middle of decimal expansion of k^k.

Original entry on oeis.org

1, 6, 888, 1808, 2138, 65246, 268105

Offset: 1

Farideh Firoozbakht, Oct 04 2013

a(6) is greater than 50000.

a(8) > 600000. - Giovanni Resta, Oct 08 2013

			6 is in the sequence because 6^6 = 46656, which includes a 6 in the middle.
11 is not in the sequence, because even though the substring 11 appears twice in 11^11 = 285311670611, neither occurrence is precisely in the middle.

Cf. A033147, A049329, A131495.

Do[a = IntegerDigits[n^n]; b = Length[a]; c = IntegerLength[n]; If[EvenQ[b - c] && FromDigits[Take[a, {(b - c)/2 + 1, (b + c)/2}]] == n, Print[n]], {n, 50000}]

is(n)=my(d=digits(n),D=digits(n^n)); if((#d+#D)%2, return(0)); for(i=1,#d, if(d[i]!=D[#D/2-#d/2+i], return(0))); 1 \\ Charles R Greathouse IV, Jul 30 2016

from itertools import islice
def A229629(): # generator of terms
    n = 1
    while True:
        s, sn = str(n**n), str(n)
        l, ln = len(s), len(sn)
        if (ln-l) % 2 == 0 and s[l//2-ln//2:l//2+(ln+1)//2] == sn: yield n
        n += 1
A229629_list = list(islice(A229629(),5)) # Chai Wah Wu, Nov 21 2021

a(6)-a(7) from Giovanni Resta, Oct 08 2013

A337904 Numbers k such that the decimal expansion of the k-th harmonic number starts with the digits of k, in the same order.

Original entry on oeis.org

1, 43, 714, 715, 9763, 122968, 122969, 1478366, 17239955, 196746419, 2209316467, 24499118645, 268950072605

Offset: 1

Metin Sariyar, Sep 29 2020

The sequence also includes 196746419, 2209316467, 24499118645, 268950072605, 2928264676792, 31663398162514, 340383084842938, 3640820101879826. - Daniel Suteu, Oct 01 2020

			1/1 + 1/2 + 1/3 + ... + 1/1478366 = 14.78366... .

Cf. A033147, A055980.

s=0;Do[s=s+(1/n);t=IntegerLength[n];m=IntegerLength[Floor[s]];k = Floor[s (10^(t-m))];If[k==n,Print[n]],{n,1,10^11}]

lista(nn) = {my(s=0.); for (n=1, nn, s += 1./n; my(d = digits(floor(10^20*s))); if (fromdigits(vector(#Str(n), j, d[j])) == n, print1(n, ", ")););} \\ Michel Marcus, Sep 30 2020

a(9) from Jinyuan Wang, Sep 30 2020
a(10)-a(12) from Chai Wah Wu, Oct 12 2020
a(13) from Chai Wah Wu, Oct 14 2020

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A383322 Lexicographically earliest sequence of distinct terms such that replacing each term k with k! does not change the succession of digits.

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A229629 Numbers k such that k is in the middle of decimal expansion of k^k.

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A337904 Numbers k such that the decimal expansion of the k-th harmonic number starts with the digits of k, in the same order.

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Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions