The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A096067

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A096067

Number of 3-smooth numbers between successive numbers that are powers of 2 or of 3.
(history; published version)

#19 by Alois P. Heinz at Fri Dec 17 09:50:23 EST 2021

STATUS

editing

approved

#18 by Alois P. Heinz at Fri Dec 17 09:50:21 EST 2021

KEYWORD

nonn,look,changed

STATUS

approved

editing

#17 by Alois P. Heinz at Fri Dec 17 09:49:58 EST 2021

STATUS

proposed

approved

#16 by Jean-François Alcover at Fri Dec 17 09:48:37 EST 2021

STATUS

editing

proposed

#15 by Jean-François Alcover at Fri Dec 17 09:48:31 EST 2021

MATHEMATICA

spi[n_] := Sum[Floor@Log[2, n/3^k] + 1, {k, 0, Floor@Log[3, n]}];

seq[n_] := Module[{a = Table[0, {n}], p = 1, s = 1}, For[i = 1, i <= Length[a], i++, p = Min[2^(1 + Floor@Log[2, p]), 3^(1 + Floor@Log[3, p])]; With[{t = spi[p]}, a[[i]] = t - s - 1; s = t]]; a];

seq[100] (* Jean-François Alcover, Dec 17 2021, after Andrew Howroyd's PARI code *)

STATUS

approved

editing

#14 by OEIS Server at Tue Jan 07 13:01:25 EST 2020

LINKS

Andrew Howroyd, <a href="/A096067/b096067_1.txt">Table of n, a(n) for n = 1..10000</a>

#13 by Peter Luschny at Tue Jan 07 13:01:25 EST 2020

STATUS

proposed

approved

Discussion

Tue Jan 07

13:01

OEIS Server: Installed new b-file as b096067.txt.  Old b-file is now b096067_1.txt.

#12 by Andrew Howroyd at Tue Jan 07 12:58:40 EST 2020

STATUS

editing

proposed

#11 by Andrew Howroyd at Tue Jan 07 12:53:59 EST 2020

LINKS

Andrew Howroyd, <a href="/A096067/b096067_1.txt">Table of n, a(n) for n = 1..100010000</a>

PROG

(PARI) \\ here mkS returns vector of A003586 with values <= limit.

(PARI) \\ here spi(n) is A071521(n).

spi(n)={sum(k=0, logint(n, 3), logint(n\3^k, 2)+1)}

mkSseq(limn)={my(S=[1]); forprime(p=2, 3, Sa=concat(vector(n), p=1, s=1); for(i=1, #a, p=min(2^(1+logint(p, 2)), 3^(1+logint(lim, p, 3))), i, [t | ; my(t<-=spi(p^()); a[i]=t-s-1)*S, ; s=t<=lim]))); Set(S)a} \\ _Andrew Howroyd_, Jan 07 2020

seq(n)={my(S=mkS(2^n), v=vector(n), k=1, p=1); for(i=1, #S, my(t=S[i]); if(isprimepower(t) && k<=#v, v[k]=i-p-1; k++; p=i)); v} \\ Andrew Howroyd, Jan 06 2020

CROSSREFS

Cf. A003586, A006899, A071521.

STATUS

approved

editing

Discussion

Tue Jan 07

12:58

Andrew Howroyd: better program (uses less memory, simpler) and more terms.

#10 by Alois P. Heinz at Tue Jan 07 04:43:31 EST 2020

STATUS

reviewed

approved