A371879 - OEIS

A371879

Prime numbers that yield a squarefree semiprime when any digit is removed.

557, 577, 587, 857, 877, 1559, 4111, 4973, 5051, 5119, 5519, 5591, 6299, 6679, 6871, 6899, 6949, 7213, 7789, 7949, 7993, 8669, 8699, 9133, 9221, 9551, 9749, 10111, 10799, 11119, 11149, 11159, 11411, 11959, 12073, 12119, 13337, 13397, 13829, 14411, 15137, 15461

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OFFSET

1,1

COMMENTS

The smallest prime with this property is 557. Since being primes, the terms of this sequence end in 1, 3, 7 or 9 and the penultimate digit is never 0, otherwise by eliminating the last digit the resulting number is not semiprime.

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

857 is a term, because it is a prime number such that if the 8 is removed, the result is 57 = 3 * 19, while if the 5 is removed, the result is 87 = 3 * 29 and if the 7 is removed, the result is 85 = 5 * 17.

MATHEMATICA

semiPrimeQ[n_] := FactorInteger[n][[;; , 2]] == {1, 1}; q[n_] := AllTrue[FromDigits@ Drop[IntegerDigits[n], {#}] & /@ Range[IntegerLength[n]], semiPrimeQ]; Select[Prime[Range[2000]], q] (* Amiram Eldar, May 26 2024 *)

PROG

(Python)

from sympy import factorint, isprime

def ok(n):

if n < 10 or not isprime(n): return False

s = str(n)

for i in range(len(s)):

ti = int(s[:i] + s[i+1:])

f = factorint(ti)

if not len(f) == 2 == sum(f.values()):

return False

return True