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

1,1

Links

Table of n, a(n) for n=1..12.

Example

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).

Prog

(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))

Crossrefs

A subset of A006567.

Sequence in context: A158723 A211116 A107288 * A342706 A095379 A350095

Adjacent sequences: A335729 A335730 A335731 * A335733 A335734 A335735

Keyword

base,nonn,fini,full,less

Author

Ray G. Opao, Jun 20 2020

Status

approved