

A372559


a(n) is the index of the first occurrence of n in A371091.


2



0, 1, 3, 9, 21, 51, 111, 321, 741, 2001, 4311, 8931, 22791, 52821, 112881, 293061, 803571, 1824591, 4887651, 14587341, 33986721, 92184861, 208581141, 431674011, 877859751, 2216416971, 4893531411, 11363224641, 24302611101, 63120770481, 140757089241, 341317579371, 742438559631, 1945801500411, 4352527381971, 11773265516781
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OFFSET

0,3


COMMENTS

The pattern in the primorial base expansion (A049345) of the terms is constructed recursively, so that the digitpositions of the primorial base expansion are successively filled with the positive terms of this sequence (1, 3, 9, 21, ...), up to that term that still fits to the position, i.e., is less than prime(i), for the positions i >= 1 indexed from the least significant end of the expansion. The nonleading digits are "frozen", and only the most significant digit keeps on increasing from a(1) to the maximal allowed a(x) for its position, after which the next term's expansion is obtained by prepending 1 to the front. See the examples.


LINKS



FORMULA



EXAMPLE

n, a(n) in primorial base
0, 0 = 0
1, 1 = 1
2, 3 = 11
3, 9 = 111
4, 21 = 311 (3 is less than prime(3)=5, so can be used now)
5, 51 = 1311 (9 cannot yet be used, so append 1 to the front)
6, 111 = 3311 (and then replace by next higher term that fits)
7, 321 = 13311
8, 741 = 33311
9, 2001 = 93311 (9 is less than prime(5)=11, so can be used now)
10, 4311 = 193311
11, 8931 = 393311
12, 22791 = 993311
13, 52821 = 1993311
14, 112881 = 3993311
15, 293061 = 9993311
16, 803571 = 19993311
17, 1824591 = 39993311
18, 4887651 = 99993311
19, 14587341 = 199993311
20, 33986721 = 399993311
21, 92184861 = 999993311
22, 208581141 = {21}99993311 (21 is less than prime(9)=23, so can be used now)
23, 431674011 = 1{21}99993311
etc.


PROG

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A235224(n) = { my(s=0, p=2); while(n, s++; n = n\p; p = nextprime(1+p)); (s); };
A276153(n) = { my(p=2, d=0); while(n, d = n%p; n = n\p; p = nextprime(1+p)); (d); };
memoA372559 = Map();
A372559(n) = if(n<=2, n+(n>1), my(v); if(mapisdefined(memoA372559, n, &v), v, my(prev=A372559(n1), hi=A235224(prev), hd=A276153(prev), k=0, u); while(A372559(k)<hd, k++); u = A372559(1+k); v = if(u>=prime(hi), prev+A002110(hi), prev+((uhd)*A002110(hi1))); mapput(memoA372559, n, v); (v)));


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



