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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The pattern in the primorial base expansion (A049345) of the terms is constructed recursively, so that the digit-positions 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 Antti Karttunen, Table of n, a(n) for n = 0..1001 Index entries for sequences related to primorial base FORMULA For n >= 0, A371091(a(n)) = n, and for all k < a(n), A371091(k) < n. 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(n-1), hi=A235224(prev), hd=A276153(prev), k=0, u); while(A372559(k)=prime(hi), prev+A002110(hi), prev+((u-hd)*A002110(hi-1))); mapput(memoA372559, n, v); (v))); CROSSREFS Positions of records in A371091. Cf. A002110, A235224, A276153. Sequence in context: A119917 A111209 A262444 * A109755 A348403 A005254 Adjacent sequences: A372556 A372557 A372558 * A372560 A372561 A372562 KEYWORD nonn,base AUTHOR Antti Karttunen, May 11 2024 STATUS approved

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Last modified September 10 06:17 EDT 2024. Contains 375773 sequences. (Running on oeis4.)