A048398 Primes with consecutive digits that differ exactly by 1.

2, 3, 5, 7, 23, 43, 67, 89, 101, 787, 4567, 12101, 12323, 12343, 32321, 32323, 34543, 54323, 56543, 56767, 76543, 78787, 78989, 210101, 212123, 234323, 234343, 432121, 432323, 432343, 434323, 454543, 456767, 654323, 654343, 678767, 678989

Offset: 1

Author

Patrick De Geest, Apr 15 1999

Keywords

• nonn
• base

Comments

Or, primes in A033075. - Zak Seidov, Feb 01 2011

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 67, p. 23, Ellipses, Paris 2008.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..1500 from Zak Seidov)

Crossrefs

Cf. A033075, A048399-A048405, A052016, A052017, A006055.

Cf. A010051; intersection of A033075 and A000040.

Programs

Haskell

a048398 n = a048398_list !! (n-1)
a048398_list = filter ((== 1) . a010051') a033075_list
-- Reinhard Zumkeller, Feb 21 2012, Nov 04 2010
(Python 3.2 or higher)
from itertools import product, accumulate
from sympy import isprime
A048398_list = [2,3,5,7]
for l in range(1,17):
    for d in [1,3,7,9]:
        dlist = [d]*l
        for elist in product([-1,1],repeat=l):
            flist = [str(d+e) for d,e in zip(dlist,accumulate(elist)) if 0 <= d+e < 10]
            if len(flist) == l and flist[-1] != '0':
                n = 10*int(''.join(flist[::-1]))+d
                if isprime(n):
                    A048398_list.append(n)
A048398_list = sorted(A048398_list) # Chai Wah Wu, May 31 2017

Mathematica

Select[Prime[Range[10000]], # < 10 || Union[Abs[Differences[IntegerDigits[#]]]] == {1} &]