The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077716 a(1) = 19; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists. 4
19, 419, 5419, 35419, 435419, 80435419, 30000080435419, 1030000080435419, 91030000080435419, 20091030000080435419, 720091030000080435419, 50720091030000080435419, 650720091030000080435419, 10650720091030000080435419, 2000000010650720091030000080435419 (list; graph; refs; listen; history; text; internal format)



a(n) is the smallest prime obtained by prefixing a(n-1) with a number of the form d*10^k where d is a single digit, 0 < d < 10, and k >= 0. Conjecture: d*10^k always exists.


Michael S. Branicky, Table of n, a(n) for n = 1..51


a:= proc(n) option remember; local k, m, d, p;

if n=1 then 19 else k:= a(n-1);

for m from length(k) do

for d to 9 do p:= k +d*10^m;

if isprime(p) then return p fi

od od



seq(a(n), n=1..20); # Alois P. Heinz, Jan 12 2015



from sympy import isprime

from itertools import islice

def agen(an=19):

while True:

yield an

pow10 = 10**len(str(an))

while True:

found = False

for t in range(pow10+an, 10*pow10+an, pow10):

if isprime(t):

an = t; found = True; break

if found: break

pow10 *= 10

print(list(islice(agen(), 15))) # Michael S. Branicky, Jun 23 2022


Cf. A069612, A077713, A077714, A077715.

Sequence in context: A202040 A244765 A069612 * A089573 A284332 A121938

Adjacent sequences: A077713 A077714 A077715 * A077717 A077718 A077719




Amarnath Murthy, Nov 19 2002


More terms from Ray Chandler, Jul 23 2003

Definition clarified by N. J. A. Sloane, Jan 19 2015



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 07:59 EST 2022. Contains 358362 sequences. (Running on oeis4.)