A355458 Numbers k that set a new record m where m is the largest left-truncatable prime up to the final k (stop on reaching the final k).

1, 7, 111, 3367, 7787, 8517, 9071, 54079, 54451, 138657, 262157, 759461, 857817, 4662317, 21754021, 25400729, 41171387, 50304331, 368119693, 799245603, 938577991

Offset

1,2

Comments

If instead of comparing the values of m, we compare the number of digits concatenated to k, then there are only 3 known terms: 1, 7 and 50304331 with 19, 23 and 24 digits respectively.

Links

Table of n, a(n) for n=1..21.

Example

a(1) = 1 because 1 sets a record m = 89726156799336363541 and 89726156799336363541, 9726156799336363541, 726156799336363541, 26156799336363541, 6156799336363541, 156799336363541, 56799336363541, 6799336363541, 799336363541, 99336363541, 9336363541, 336363541, 36363541, 6363541, 363541, 63541, 3541, 541, 41 are all primes (the truncation stops when the final k is reached).
a(2) = 7 because for k = 2..6 no m exceeds 89726156799336363541, but for k = 7, m = 357686312646216567629137.

Prog

(Python)
from sympy import isprime
def findNewCandidates(candidates):
  newCandidates = []
  for candidate in candidates:
    for k in range(1, 10):
      p = int(str(k) + str(candidate))
      if (isprime(p)):
        newCandidates.append(p)
  return newCandidates
record = 0
for k in range(1, 10**6):
  if (k % 2 == 0 or k % 5 == 0):
    continue
  toCheck = [k]
  while len(toCheck) > 0:
    lastToCheck = toCheck
    toCheck = findNewCandidates(toCheck)
  result = lastToCheck[-1]
  if (result > record):
    record = result
    print(str(k))

Crossrefs

Cf. A024785.

Sequence in context: A009471 A301990 A193441 * A260027 A061233 A117795

Adjacent sequences: A355455 A355456 A355457 * A355459 A355460 A355461

Keyword

nonn,base,more

Author

Eder Vanzei, Jul 02 2022

Extensions

a(15)-a(18) from Michael S. Branicky, Jul 02 2022

a(19)-a(21) from Michael S. Branicky, Jul 04 2022

Status

approved