A180101 -id:A180101 - cp's OEIS frontend

A180107 Partial sums of terms in A180101.

0, 1, 1, 2, 4, 6, 9, 12, 15, 20, 25, 30, 35, 42, 49, 56, 63, 70, 77, 88, 99, 110, 121, 132, 143, 156, 169, 182, 195, 208, 221, 238, 255, 272, 289, 306, 323, 342, 361, 380, 399, 418, 437, 460, 483, 506, 529, 552, 575, 598, 621, 644, 667, 696, 725, 754, 783, 812, 841, 870, 899, 930, 961, 992, 1023, 1054, 1085, 1116, 1147, 1184, 1221, 1258, 1295, 1332, 1369, 1406, 1443, 1480, 1517, 1558, 1599, 1640

Offset: 0

N. J. A. Sloane, Jan 16 2011

nonn

Apart from initial terms, same as A036441 and A076271, but the simple definition warrants an independent entry.

T. D. Noe, Table of n, a(n) for n = 0..10000

Cf. A180101, A036441, A076271.

A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor".

Original entry on oeis.org

1, 1, 2, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5

Offset: 1

N. J. A. Sloane, Dec 16 2010

nonn

Rapidly enters a loop with period 3,5,2,7.

More generally, if a(1) and a(2) are distinct positive numbers with a(1)+a(2) >= 2, the sequence eventually enters the cycle {7,3,5,2} [Back and Caragiu].

G. Back and M. Caragiu, The greatest prime factor and recurrent sequences, Fib. Q., 48 (2010), 358-362.

Cf. A000045, A006530, A020639.

Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183.

nxt[{a_,b_}]:={b,FactorInteger[a+b][[-1,1]]}; Transpose[NestList[nxt,{1,1},120]][[1]] (* or *) PadRight[{1,1,2},130,{5,2,7,3}] (* Harvey P. Dale, Feb 24 2015 *)

A076272 Largest prime factor of A076271(n): A006530(A076271(n)).

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 37, 37

Offset: 1

Reinhard Zumkeller, Oct 04 2002

nonn

T. D. Noe, Table of n, a(n) for n = 1..10000

See A180101 for a variant.

Differences[NestList[#+FactorInteger[#][[-1,1]]&,1,100]] (* Paolo Xausa, Dec 09 2023 *)

a(n) = A076271(n+1) - A076271(n) for all n;

a(A076273(k)+j) = A008578(k) for k>0 and 0 <= j < A075527(k-1).

cp's OEIS Frontend

A180107 Partial sums of terms in A180101.

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A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor".

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A076272 Largest prime factor of A076271(n): A006530(A076271(n)).

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