A064489 -id:A064489 - cp's OEIS frontend

A064490 Smallest prime with prime(n) decimal digits.

11, 101, 10007, 1000003, 10000000019, 1000000000039, 10000000000000061, 1000000000000000003, 10000000000000000000009, 10000000000000000000000000331, 1000000000000000000000000000057, 1000000000000000000000000000000000067, 10000000000000000000000000000000000000121

Offset: 1

Jason Earls, Oct 04 2001

			11 is the first prime with 2 decimal digits.
101 is the first prime with 3 decimal digits.

Alois P. Heinz, Table of n, a(n) for n = 1..168 (first 75 terms from Harry J. Smith)

Cf. A000040, A003617, A064489.

for n from 1 to 20 do p := ithprime(n): for i from 10^(p-1) to 10^p do if isprime(i) then printf(`%d,`,i); break; fi: od: od:
# second Maple program:
a:= n-> nextprime(10^(ithprime(n)-1)):
seq(a(n), n=1..15);  # Alois P. Heinz, Jun 24 2018

Table[NextPrime[10^(n-1)],{n,Prime[Range[15]]}] (* Harvey P. Dale, Feb 06 2020 *)

l(n)=ln=0; while(n,n=floor(n/10); ln++); return(ln);
a=0; for(n=1,10^6,x=l(prime(n)); if(isprime(x),b=x; if(b>a,a=b; print(prime(n)))))

{ for (n=1, 75, p=prime(n); a=nextprime(10^(p - 1)); write("b064490.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 16 2009

from sympy import prime, nextprime, primepi
def a(n): return nextprime(10**(prime(n)-1))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, May 26 2021

a(n) = A003617(A000040(n)).

a(n) = A000040(A064489(n)).

More terms from James Sellers, Oct 08 2001

Offset changed from 0 to 1 by Harry J. Smith, Sep 16 2009

A126712 Height of steps in Recamán's sequence A064389.

Original entry on oeis.org

0, 1, 1, 4, 4, 2, 2, 3, 3, 3, 3, 3, 3, 7, 5, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 7, 5, 5, 5, 11, 11, 11, 11, 11, 11, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 6, 6, 11, 9, 9, 6, 6, 11, 8, 8, 8, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

R. J. Mathar, Feb 12 2007

			The heights to reach 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24 in A064389 are b(1,2,3,...) = 0, 1, 2, 1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5 etc., as defined by b(n) = b(n-1) + sign(A064389(n) - A064389(n-1)).
Reshuffling sequence b while sorting A064489 into A078758 produces sequence a here, a(n) = b(A078758(n)).

Cf. A064389, A078758.

A064389 := proc(nmax) local a,n,adiff,newa ; a := [1] ; for n from 2 to nmax do adiff := n ; while true do newa := op(-1,a)-adiff ; if newa >0 and not newa in a then a := [op(a),newa] ; break ; fi ; newa := op(-1,a)+adiff ; if newa >0 and not newa in a then a := [op(a),newa] ; break ; fi ; adiff := adiff+1 ; od ; od ; RETURN(a) ; end: A064389b := proc(a) local n,hei ; hei := [0] ; for n from 2 to nops(a) do hei := [op(hei),op(-1,hei)+sign(op(n,a)-op(n-1,a))] ; od ; RETURN(hei) ; end: inList := proc(list,n) local i ; for i from 1 to nops(list) do if op(i,list) = n then RETURN(i) ; fi ; od ; RETURN(-1) ; end: A078758 := proc(a064389) local a,n,i ; a := [] ; n :=1 ; while true do i := inList(a064389,n) ; if i < 0 then RETURN(a) ; else a := [op(a),i] ; n := n+1 ; fi ; od ; end: nmax := 1800 : a064389 := A064389(nmax) : a078758 := A078758(a064389) : b := A064389b(a064389) : for n from 1 to nops(a078758) do printf("%d, ",op(op(n,a078758),b)) ; od;

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A064490 Smallest prime with prime(n) decimal digits.

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