This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(2) = 2 since 31 and 37 are the only two 2-digit primes beginning with prime(2) = 3.
A088754(n)={ local (resul,sdig,p,lo,hi) ; sdig=prime(n) ; lo=sdig ; hi=sdig+1 ; while( lo < 10^(n-1), lo *= 10 ; hi *= 10 ; ) ; resul=0 ; p=nextprime(lo) ; while(p < hi, resul++ ; p=nextprime(p+1) ; ) ; return(resul) ; } { for(n=1,11, print(A088754(n)); ) } \\ R. J. Mathar, Sep 25 2006
from sympy import prime, primepi def A088754(n): p = prime(n) m = n-len(str(p)) return primepi((p+1)*10**m)-primepi(p*10**m) # Chai Wah Wu, Jun 18 2019
a(5) = 50021 - 50000 = 21.
a(6) =3 = 130003 - 130000.
a(2) = 2 since 23 and 29 are the only two 2-digit primes beginning with 2.
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.
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 *)
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;
}
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