A083289 Least k such that 10^n+k is a brilliant number (cf. A078972).

3, 0, 21, 3, 201, 13, 18081, 43, 140049, 81, 600009, 147, 6000009, 73, 380000361, 3, 1400000049, 831, 14000000049, 49, 380000000361, 987, 600000000009, 691, 78000000001521, 183, 740000000001369, 4153, 6200000000000961, 279

Offset

0,1

Comments

If n is an even positive exponent, then a(n) is the first prime greater than 10^(n/2) squared less 10^n.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..42

Dario Alejandro Alpern, Brilliant numbers

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; LengthBase10[n_] := Floor[ Log[10, n] + 1]; f[n_] := Block[{k = 0}, If[ EvenQ[n] && n > 1, NextPrim[ 10^(n/2)]^2 - 10^n, While[fi = FactorInteger[10^n + k]; Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ fi] != 2 || Length[ Union[ LengthBase10 /@ Flatten[ Table[ # [[1]], {1}] & /@ fi]]] != 1, k++ ]; k]]; Table[ f[n], {n, 0, 30}]

Prog

(Python)
from sympy import nextprime, factorint
def A083289(n):
    a, b = divmod(n, 2)
    c, d = 10**n, 10**a
    if b == 0: return nextprime(d)**2-c
    k = 0
    while True:
        fs = factorint(c+k, multiple=True)
        if len(fs) == 2 and min(fs) >= d:
            return k
        k += 1 # Chai Wah Wu, Sep 28 2021

Crossrefs

Cf. A078972, A084475, A084476.

Sequence in context: A215583 A215678 A186747 * A108196 A370015 A328341

Adjacent sequences: A083286 A083287 A083288 * A083290 A083291 A083292

Keyword

base,nonn

Author

Jason Earls, Jun 03 2003

Extensions

Edited and extended by Robert G. Wilson v, Jun 27 2003

Status

approved