A068896 Primes containing 2k digits in which the sum of the first k digits is that of the last k digits.

11, 1423, 1607, 1753, 1973, 2011, 2213, 2341, 2543, 2617, 2671, 2819, 2837, 3407, 3461, 3517, 3571, 3719, 3847, 4013, 4637, 4673, 4691, 4729, 4783, 4967, 5023, 5261, 5519, 5573, 5591, 5647, 5683, 5849, 5867, 6143, 6217, 6271, 6473, 6491, 6529, 6547, 7043, 7649, 7759, 8017, 8053, 8219, 8237, 8273, 8291, 8329, 8677, 9137, 9173, 9283, 9467

Offset: 1

Author

Amarnath Murthy, Mar 21 2002

Keywords

• easy
• nonn
• base

Examples

			2341 is a member with 2+3 = 4+1.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A240927.

Programs

Mathematica

Select[Prime[Range[169,1229]],Length[Union[Total/@TakeDrop[ IntegerDigits[ #],2]]] == 1&] (* The program generates all 56 4-digit terms. To generate all 3669 of the 6-digit terms, change the Range constants to (9593, 78498) and change the 2 to 3. *) (* Harvey P. Dale, Aug 15 2021 *)

Python

from sympy import primerange
def sd(s): return sum(map(int, s))
def auptod(digits):
    alst = []
    for d in range(2, digits+1, 2):
        for p in primerange(10**(d-1), 10**d):
            s = str(p)
            if sd(s[:len(s)//2]) == sd(s[len(s)//2:]): alst.append(p)
    return alst
print(auptod(4)) # Michael S. Branicky, Aug 15 2021

Extensions

Corrected and extended by Harvey P. Dale, Aug 15 2021

11 prepended by David A. Corneth, Aug 15 2021