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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)
OFFSET

1,1

COMMENTS

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.

LINKS

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

MAPLE

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

fi

end:

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

PROG

(Python)

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

CROSSREFS

Cf. A069612, A077713, A077714, A077715.

Sequence in context: A202040 A244765 A069612 * A089573 A284332 A121938

Adjacent sequences: A077713 A077714 A077715 * A077717 A077718 A077719

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Nov 19 2002

EXTENSIONS

More terms from Ray Chandler, Jul 23 2003

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

STATUS

approved

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