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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 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.)