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A276154 a(n) = Shift primorial base representation (A049345) of n left by one digit (append one zero to the right, then convert back to decimal). 15

%I #28 Mar 18 2021 23:39:41

%S 0,2,6,8,12,14,30,32,36,38,42,44,60,62,66,68,72,74,90,92,96,98,102,

%T 104,120,122,126,128,132,134,210,212,216,218,222,224,240,242,246,248,

%U 252,254,270,272,276,278,282,284,300,302,306,308,312,314,330,332,336,338,342,344,420,422,426,428,432,434,450,452,456,458,462,464,480,482,486,488

%N a(n) = Shift primorial base representation (A049345) of n left by one digit (append one zero to the right, then convert back to decimal).

%H Antti Karttunen, <a href="/A276154/b276154.txt">Table of n, a(n) for n = 0..30029</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(0) = 0; for n >= 1, a(n) = A276152(n) + a(A276151(n)).

%F a(n) = A276085(A003961(A276086(n))). - _Antti Karttunen_, Mar 15 2021

%e n A049345 with one zero converted back

%e appended to the right to decimal = a(n)

%e ---------------------------------------------------------

%e 0 0 00 0

%e 1 1 10 2

%e 2 10 100 6

%e 3 11 110 8

%e 4 20 200 12

%e 5 21 210 14

%e 6 100 1000 30

%e 7 101 1010 32

%e 8 110 1100 36

%e 9 111 1110 38

%e 10 120 1200 42

%e 11 121 1210 44

%e 12 200 2000 60

%e 13 201 2010 62

%e 14 210 2100 66

%e 15 211 2110 68

%e 16 220 2200 72

%t nn = 75; b = MixedRadix[Reverse@ Prime@ NestWhileList[# + 1 &, 1, Times @@ Prime@ Range[#] <= nn &]]; Table[FromDigits[#, b] &@ Append[IntegerDigits[n, b], 0], {n, 0, nn}] (* Version 10.2, or *)

%t f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], Times @@ Prime@ Range[# - i]]], {i, 0, #}] &@ NestWhile[# + 1 &, 0, Times @@ Prime@ Range[# + 1] <= n &]; Rest[a][[All, 1]]]; Table[Total[Times @@@ Transpose@ {Map[Times @@ # &, Prime@ Range@ Range[0, Length@ # - 1]], Reverse@ #}] &@ Append[f@ n, 0], {n, 0, 75}] (* _Michael De Vlieger_, Aug 26 2016 *)

%o (PARI) A276154(n) = A276085(A003961(A276086(n))); \\ _Antti Karttunen_, Mar 15 2021

%o (PARI)

%o A276151(n) = { my(s=1); forprime(p=2, , if(n%p, return(n-s), s *= p)); };

%o A276152(n) = { my(s=1); forprime(p=2, , if(n%p, return(s*p), s *= p)); };

%o A276154(n) = if(!n,n,(A276152(n) + A276154(A276151(n)))); \\ _Antti Karttunen_, Mar 15 2021

%o (Scheme) (definec (A276154 n) (if (zero? n) n (+ (A276152 n) (A276154 (A276151 n)))))

%Y Complement: A276155.

%Y Cf. A002110, A003961, A049345, A276085, A276086, A276151, A276152, A286629 [= a(A061720(n-1))], A324384 [= gcd(n, a(n))], A323879, A328770 (a subsequence).

%Y Cf. also A276156, A328461, A328464.

%Y Dispersion array and its transpose: A276943, A276945, with primorials divided out: A286623, A286625.

%Y Analogous to A153880.

%K nonn,base

%O 0,2

%A _Antti Karttunen_, Aug 24 2016

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)