A335732 - OEIS

%I #28 Jan 15 2023 19:49:47

%S 13,31,79,97,347,709,743,769,907,967,1847,7481

%N Emirps whose concatenation of adjacent digit differences either form an emirp that also has this characteristic or form a single-digit prime, and whose emirp also has this characteristic.

%e 7481 is in the list as the concatenation of adjacent digit differences forms an emirp (i.e., |7-4|=3; |4-8|=4; |8-1|=7; which form 347, which is an emirp as 743 is also prime). Furthermore, for 347, |3-4|=1; |4-7|=3; forms 13, which is an emirp as 31 is also prime. Finally, |1-3| = 2, which is prime. This characteristic is also true for the emirp of 7481 which is 1847 (i.e., 1847 forms 743 which forms 31 which finally forms 2).

%o (Python)

%o from sympy.ntheory import isprime as isp

%o i = []

%o for a in range(10,1000000):

%o     if isp(a):

%o         b = str(a)

%o         d=[]

%o         for c in range(0,len(b)-1):

%o             ee = abs(int(b[c])-int(b[c+1]))

%o             d.append(str(ee))

%o         f = ''.join(d)

%o         g = b[::-1]

%o         if isp(int(f)) and isp(int(g)):

%o             if len(b)<3:

%o                 i.append(b)

%o             else:

%o                 if f in i:

%o                     i.append(b)

%o print(','.join(i))

%Y A subset of A006567.

%K base,nonn,fini,full,less

%O 1,1

%A _Ray G. Opao_, Jun 20 2020