A323026 Zeroless pandigital numbers that are between two twin primes.

123457968, 123459768, 123946578, 124397658, 124936578, 124953678, 125347698, 125437968, 125463798, 125674398, 126345978, 126495738, 126593478, 126597348, 126945738, 127394568, 127396458, 127453968, 127459638, 127659438, 129357648, 129635478, 129673548, 132564978, 132594768, 132769458

Offset: 1

Author

Pierandrea Formusa, Jan 02 2019

Keywords

• nonn
• base

Comments

Intersection of A050289 and A014574.

The definition permits repeated digits. - N. J. A. Sloane, May 16 2023

a(n) mod 10 is either 2 or 8. First term with a(n) mod 10 = 2 is a(27) = 134756982. - Chai Wah Wu, Jan 27 2019

There are 2595 terms that are pandigital without repeating any digit. - Harvey P. Dale, Jan 25 2021

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050289 (zeroless pandigital numbers), A014574 (average of twin primes).

Programs

PARI

isok(n) = my(d=digits(n)); vecmin(d) && (#Set(d)==9) && isprime(n-1) && isprime(n+1);
for (n=123456789, 133000000, if (isok(n), print1(n, ", "))) \\ Michel Marcus, Jan 04 2019

Python

import itertools
from sympy import isprime
nmax=pow(10,10)
r=""
li=[]
def is_pandigit_easy(n):
    l=[]
    s=str(n)
    if '0' in s: return(False)
    for ch in s:
        if ch not in l: l.append(ch)
    l=list(set(l))
    if len(l)==9:
        return(True)
    else:
        return(False)
t=0
tmax=50
for i in range(123456789,nmax):
    if is_pandigit_easy(i):
        if isprime(i-1) and isprime(i+1):
            li.append(i)
            t+=1
            if t>tmax: break
first_elem=26
for k in li[:first_elem]:
      r=r+","+str(k)
print(r[1:])

Python

from itertools import permutations
from sympy import isprime
A323026_list = [n for n in (int(''.join(s)) for s in permutations('123456789')) if isprime(n-1) and isprime(n+1)] # Chai Wah Wu, Jan 27 2019