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 A225903 The smallest number beginning with n whose distinct prime factors are the first n primes. 2
 16, 24, 30, 420, 50820, 60060, 7147140, 87297210, 9369900540, 103515091680, 11030826957150, 126152548291770, 13387011595197240, 143910374648370330, 15372244564712285250, 162945792385950223650, 17304843151387913751630, 1876614101750511535732320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(3)=30 is the only term with fewer than 1000 digits whose superscripts are all 1. Though counterexamples are possible, it appears that the sequence is strictly increasing (confirmed for n < 350, and counterexamples are increasingly unlikely statistically thereafter). LINKS Christian N. K. Anderson, Table of n, a(n) for n = 1..349 EXAMPLE For a(6), the number 60060 = 2^2 * 3 * 5 * 7 * 11 * 13. The only number smaller whose factors contains the first 6 primes is 30030, which does not begin with 6. MATHEMATICA a[n_] := Block[{p = Prime[n], ba = Product[Prime@k, {k, n}], d = IntegerDigits@ n, mu = 1}, While[d != Take[IntegerDigits[mu*ba], Length@d] || Max[ First /@ FactorInteger[mu]] > p, mu++]; mu*ba]; Array[a, 20] (* Giovanni Resta, May 27 2013 *) PROG (R) library(gmp); primes<-function(n) { x=as.bigz(rep(2, n)); for(i in 2:n) x[i]=nextprime(x[i-1]); as.vector(x[1:n]) } newmin<-function(b, d) { if(d>length(b)) return();     while(1) { b[d]=b[d]+1; if((x=prod(pr^b))>v) return()         if(substr(x, 1, ndig(i))==as.character(i)) { v<<-x; return() }         if(b[d]==2) {b[d]=1; newmin(b, d+1); b[d]=2 }         newmin(b, d+1)     } } y=as.bigz(rep(0, 50)) for(i in 1:50) {     pr=primes(i); b=rep(1, i)     while(substr((v=prod(pr^b)), 1, ndig(i))!=as.character(i)) b[1]=b[1]+1;     while(b[1]>1) { b[1]=b[1]-1; newmin(b, 2) }     if(y[i]>v) y[i]=v; } CROSSREFS Cf. A000040, A002110. Cf. A086558, A109864, A088104 Cf. A018802, A077515, A077727 Sequence in context: A271783 A114415 A320141 * A033987 A140349 A088493 Adjacent sequences:  A225900 A225901 A225902 * A225904 A225905 A225906 KEYWORD nonn,base AUTHOR Kevin L. Schwartz and Christian N. K. Anderson, May 21 2013 STATUS approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)