A258337 -id:A258337 - cp's OEIS frontend

A258339 PrimePi(A258337(n)).

5, 1, 2, 13, 3, 18, 4, 23, 25, 26, 30, 31, 6, 35, 36, 38, 7, 42, 8, 304, 47, 48, 9, 53, 54, 56, 58, 60, 10, 63, 11, 453, 67, 69, 71, 73, 12, 76, 78, 79, 81, 82, 14, 86, 88, 89, 15, 93, 94, 96, 682, 98, 16, 100, 102, 103, 105, 107, 17, 110, 112, 807, 115, 116, 119, 121, 19, 124, 125, 126, 20, 129, 21, 132, 133, 135, 137, 138, 22, 140, 141, 142, 146, 1052, 147, 150

Offset: 1

Vladimir Shevelev, May 27 2015

The sequence is a permutation of the positive numbers.

Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Cf. A000720, A258337.

a(n) >= PrimePi(n).

A018800 Smallest prime that begins with n.

Original entry on oeis.org

11, 2, 3, 41, 5, 61, 7, 83, 97, 101, 11, 127, 13, 149, 151, 163, 17, 181, 19, 2003, 211, 223, 23, 241, 251, 263, 271, 281, 29, 307, 31, 3203, 331, 347, 353, 367, 37, 383, 397, 401, 41, 421, 43, 443, 457, 461, 47, 487, 491, 503, 5101, 521, 53, 541, 557, 563, 571, 587, 59

Offset: 1

David W. Wilson

Conjecture: If a(n) = (n concatenated with k) then k < n. - Amarnath Murthy, May 01 2002

a(n) always exists. Proof. Suppose n is L digits long, and consider the numbers between n*10^B and n*10^B+10^C, where B > C are both large compared with L. All such numbers begin with the digits of n. Using the upper and lower bounds on pi(x) from Theorem 1 of Rosser and Schoenfeld, it follows that for sufficiently large B and C, at least one of these numbers is a prime. QED - N. J. A. Sloane, Nov 14 2014

T. D. Noe, Table of n, a(n) for n = 1..1000 (first 100 terms from Paolo P. Lava)
J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), pp. 64-94.
Index entries for primes involving decimal expansion of n

Cf. A030665, A068164, A068695, A062584, A088781, A085608.
A164022 is the base-2 analog.
Cf. also A258337.
Row n=1 of A262369.

import Data.List (isPrefixOf, find); import Data.Maybe (fromJust)
a018800 n = read $ fromJust $
            find (show n `isPrefixOf`) $ map show a000040_list :: Int
-- Reinhard Zumkeller, Jul 01 2015

f:= proc(n) local x0, d,r,y;
   if isprime(n) then return(n) fi;
   for d from 1 do
     x0:= n*10^d;
     for r from 1 to 10^d-1 by 2 do
       if isprime(x0+r) then
          return(x0+r)
       fi
     od
   od
end proc:
seq(f(n),n=1..100); # Robert Israel, Dec 23 2014

Table[Function[d, FromDigits@ SelectFirst[ IntegerDigits@ Prime@ Range[10^4], Length@ # >= Length@ d && Take[#, Length@ d] == d &]][ IntegerDigits@ n], {n, 59}] (* Michael De Vlieger, May 24 2016, Version 10 *)

a(n{,base=10}) = for (l=0, oo, forprime (p=n*base^l, (n+1)*base^l-1, return (p))) \\ Rémy Sigrist, Jun 11 2017

from sympy import isprime
def a(n):
    if isprime(n): return n
    pow10 = 10
    while True:
        t, maxt = n * pow10 + 1, (n+1) * pow10
        while t < maxt:
            if isprime(t): return t
            t += 2
        pow10 *= 10
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Nov 02 2021

a(n) = prime(A085608(n)). - Michel Marcus, Oct 19 2013

cp's OEIS Frontend

A258339 PrimePi(A258337(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A018800 Smallest prime that begins with n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula