A276154 - OEIS

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).

0, 2, 6, 8, 12, 14, 30, 32, 36, 38, 42, 44, 60, 62, 66, 68, 72, 74, 90, 92, 96, 98, 102, 104, 120, 122, 126, 128, 132, 134, 210, 212, 216, 218, 222, 224, 240, 242, 246, 248, 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

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OFFSET

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..30029

Index entries for sequences related to primorial base

FORMULA

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

a(n) = A276085(A003961(A276086(n))). - Antti Karttunen, Mar 15 2021

EXAMPLE

n A049345 with one zero converted back

appended to the right to decimal = a(n)

---------------------------------------------------------

0 0 00 0

1 1 10 2

2 10 100 6

3 11 110 8

4 20 200 12

5 21 210 14

6 100 1000 30

7 101 1010 32

8 110 1100 36

9 111 1110 38

10 120 1200 42

11 121 1210 44

12 200 2000 60

13 201 2010 62

14 210 2100 66

15 211 2110 68

16 220 2200 72

MATHEMATICA

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 *)

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 *)

PROG

(PARI) A276154(n) = A276085(A003961(A276086(n))); \\ Antti Karttunen, Mar 15 2021

(PARI)

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

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

A276154(n) = if(!n, n, (A276152(n) + A276154(A276151(n)))); \\ Antti Karttunen, Mar 15 2021

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

CROSSREFS

Complement: A276155.

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

Cf. also A276156, A328461, A328464.

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

Analogous to A153880.

Sequence in context: A024894 A153880 A120227 * A328770 A138626 A178406

Adjacent sequences: A276151 A276152 A276153 * A276155 A276156 A276157

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Aug 24 2016

STATUS

approved