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%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
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