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A232125 Smallest prime such that the n numbers obtained by removing 1 digit on the right are also prime, while no digit can be added on the right to get another prime. 5
53, 53, 317, 2393, 23333, 373393, 2399333, 23399339, 1979339333, 103997939939, 4099339193933, 145701173999399393, 2744903797739993993333, 52327811119399399313393, 13302806296379339933399333 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Inspired by article on 43 in Archimedes' Lab link.
LINKS
G. A. Sarcone and M. J. Waeber, What's Special About This Number?, Archimedes' Lab website.
EXAMPLE
a(0)=53 because 53 is the smallest prime such that all numbers obtained by adding a digit to the right are composite.
a(1)=53 because 5 and 53 are primes.
a(2)=317 because 3, 31, 317 are all primes, and 317 has the same property as 53 when adding a digit to the right.
PROG
(PARI) a(n) = {n++; v = vector(n); i = 1; ok = 0; until (ok, while ((i>1) && (v[i] == 9), v[i] = 0; i--); if (i == 1, v[i] = nextprime(v[i]+1), v[i] = v[i]+1); curp = sum (j=1, i, v[j]*(10^(i-j))); if (isprime(curp), if (i != n, i++, nbp = 0; for (z=1, 9, if (isprime(10*curp+z), nbp++); ); if (nbp == 0, ok = 1); ); ); ); sum (j=1, n, v[j]*(10^(n-j))); }
(Python)
from sympy import isprime, nextprime
def a(n):
p, oo = 2, float('inf')
while True:
extends, reach, r1 = 0, [str(p)], []
while len(reach) > 0 and extends <= n:
minnotext = oo
for s in reach:
wasextended = False
for d in "1379":
if isprime(int(s+d)): r1.append(s+d); wasextended = True
if not wasextended: minnotext = min(minnotext, int(s))
if extends == n and minnotext < oo: return minnotext
if len(r1) > 0: extends += 1
reach, r1 = r1, []
p = nextprime(p)
for n in range(12): print(a(n), end=", ") # Michael S. Branicky, Aug 08 2021
CROSSREFS
Sequence in context: A109648 A109733 A094462 * A349091 A343794 A042403
KEYWORD
nonn,base,more
AUTHOR
Michel Marcus, Nov 19 2013
EXTENSIONS
a(12)-a(13) from Michael S. Branicky, Aug 08 2021
a(14) from Michael S. Branicky, Aug 23 2021
STATUS
approved

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Last modified May 25 11:12 EDT 2024. Contains 372788 sequences. (Running on oeis4.)