A335732 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.

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

Offset: 1

Author

Ray G. Opao, Jun 20 2020

Keywords

• base
• nonn
• fini
• full
• less

Examples

			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).
		

Crossrefs

A subset of A006567.

Programs

Python

from sympy.ntheory import isprime as isp
i = []
for a in range(10,1000000):
    if isp(a):
        b = str(a)
        d=[]
        for c in range(0,len(b)-1):
            ee = abs(int(b[c])-int(b[c+1]))
            d.append(str(ee))
        f = ''.join(d)
        g = b[::-1]
        if isp(int(f)) and isp(int(g)):
            if len(b)<3:
                i.append(b)
            else:
                if f in i:
                    i.append(b)
print(','.join(i))