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 A212875 Primonacci numbers: composite numbers that appear in the Fibonacci-like sequence generated by their own prime factors. 3
 4, 9, 12, 25, 27, 169, 1102, 7921, 22287, 54289, 103823, 777627, 876897, 2550409, 20854593, 34652571, 144237401, 144342653, 167901581, 267911895, 792504416, 821223649, 1103528482, 2040412557, 2852002829, 3493254541, 6033671841, 15658859018, 116085000401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Given n, form a sequence that starts with the k prime factors of n in ascending order. After that, each term is the sum of the preceding k terms. If n eventually appears in the sequence, it is a primonacci number. Primes possess this property trivially and are therefore excluded. Similar to A007629 (repfigit or Keith numbers), but base-independent. If n is in A005478 (Fibonacci primes), then n^2 is a primonacci number. The only entries that are semiprimes (A001358) are the squares of A005478. - Robert Israel, Mar 08 2016 LINKS Herman Beeksma, Table of n, a(n) for n = 1..42 EXAMPLE Fibonacci-like sequences for selected values of n: n=12: 2, 2, 3, 7, 12, ... n=25: 5, 5, 10, 15, 25, ... n=1102: 2, 19, 29, 50, 98, 177, 325, 600, 1102, ... MAPLE with(numtheory): P:=proc(q, h) local a, b, j, k, n, t, v; v:=array(1..h); for n from 2 to q do if not isprime(n) then b:=ifactors(n)[2]; a:=[]; for k from 1 to nops(b) do for j from 1 to b[k][2] do a:=[op(a), b[k][1]]; od; od; a:=sort([op(a)]); b:=nops(a); for k from 1 to b do v[k]:=a[k]; od; t:=b+1; v[t]:=add(v[k], k=1..b); while v[t]

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Last modified June 7 20:32 EDT 2023. Contains 363157 sequences. (Running on oeis4.)