Mateusz Pasternak - cp's OEIS frontend

User: Mateusz Pasternak

Mateusz Pasternak has authored 2 sequences.

A352375 Sum of digits of A007618.

5, 1, 2, 4, 8, 7, 5, 10, 11, 13, 8, 16, 14, 10, 11, 4, 8, 7, 14, 10, 11, 13, 17, 7, 5, 10, 11, 13, 8, 16, 14, 19, 11, 13, 8, 16, 14, 19, 20, 13, 8, 16, 14, 19, 20, 13, 8, 16, 14, 19, 20, 22, 8, 16, 14, 19, 20, 22, 17, 16, 14, 19, 20, 13, 17, 16, 14, 19, 20, 13

Offset: 1

Mateusz Pasternak, Mar 14 2022

D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.

D. R. Kaprekar, The Mathematics of the New Self Numbers, 1963. [annotated and scanned]

Cf. A007618, A007953.

lista(nn) = my(s, x=5); for(n=1, nn, print1(s=sumdigits(x), ", "); x+=s); \\ Jinyuan Wang, Mar 22 2022

from itertools import islice
def A352375_gen(): # generator of terms
    a = 5
    while True:
        yield (s := sum(int(d) for d in str(a)))
        a += s
A352375_list = list(islice(A352375_gen(),20)) # Chai Wah Wu, Mar 29 2022

a(n) = A007953(A007618(n)).

a(n) = A007618(n+1)-A007618(n). - Chai Wah Wu, Mar 29 2022

More terms from Jinyuan Wang, Mar 22 2022

A297996 a(1)=2, a(2)=3, a(3)=5 and a(n) = (a(1) + a(2) + a(3) + ... + a(n-1))/a(n-1).

Original entry on oeis.org

2, 3, 5, 2, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, 27, 24, 28, 25, 29, 26, 30, 27, 31, 28, 32, 29, 33, 30, 34, 31, 35, 32, 36, 33, 37, 34, 38, 35

Offset: 1

Mateusz Pasternak, Jan 10 2018

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A168230.

Nest[Append[#, Total[#]/Last[#]] &, Prime@ Range@ 3, 67] (* Michael De Vlieger, Jan 10 2018 *)
LinearRecurrence[{1,1,-1},{2,3,5,2,6},70] (* Harvey P. Dale, Dec 31 2021 *)

lista(nn) = {va = vector(nn); for (n=1, 3, va[n] = prime(n)); for (n=4, nn, va[n] = sum(k=1, n-1, va[k])/va[n-1];); va;} \\ Michel Marcus, Jan 10 2018

Vec(x*(2 + x - 4*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)) + O(x^100)) \\ Colin Barker, Jan 29 2018

a(n) = A168230(n+1) for n >= 3.
From Colin Barker, Jan 29 2018: (Start)
G.f.: x*(2 + x - 4*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)).
a(n) = n/2 for n>2 and even.
a(n) = (n+7)/2 for n>2 and odd.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>5.
(End)

More terms from Michel Marcus, Jan 10 2018

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User: Mateusz Pasternak

A352375 Sum of digits of A007618.

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A297996 a(1)=2, a(2)=3, a(3)=5 and a(n) = (a(1) + a(2) + a(3) + ... + a(n-1))/a(n-1).

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