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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

Table of n, a(n) for n=0..14.

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

Cf. A024770, A119289, A227919, A239747.

Sequence in context: A109648 A109733 A094462 * A349091 A343794 A042403

Adjacent sequences:  A232122 A232123 A232124 * A232126 A232127 A232128

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 August 9 07:42 EDT 2022. Contains 356019 sequences. (Running on oeis4.)