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.
53, 53, 317, 2393, 23333, 373393, 2399333, 23399339, 1979339333, 103997939939, 4099339193933, 145701173999399393, 2744903797739993993333, 52327811119399399313393, 13302806296379339933399333
Offset: 0
Examples
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.
Links
- G. A. Sarcone and M. J. Waeber, What's Special About This Number?, Archimedes' Lab website.
Programs
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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
Extensions
a(12)-a(13) from Michael S. Branicky, Aug 08 2021
a(14) from Michael S. Branicky, Aug 23 2021
Comments