A066540 The first of two consecutive primes with equal digital sums.

523, 1069, 1259, 1759, 1913, 2503, 3803, 4159, 4373, 4423, 4463, 4603, 4703, 4733, 5059, 5209, 6229, 6529, 6619, 7159, 7433, 7459, 8191, 9109, 9749, 9949, 10691, 10753, 12619, 12763, 12923, 13763, 14033, 14107, 14303, 14369, 15859, 15973, 16529, 16673, 16903, 17239

Offset: 1

Author

Jason Earls, Jan 06 2002

Keywords

• base
• easy
• nonn

Comments

The difference between the two primes of the pair is a multiple of 18. - Antonio Roldán, Mar 13 2012

Examples

			a(1) = 523 because both it and the next prime, 541, have a digital sum of 10.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• G. L. Honaker, Jr. and C. Caldwell, Prime Curios!

Crossrefs

Subsequence of A117838. A069567 is a subsequence.

Cf. A007513, A007953, A209396, A210629.

Programs

Mathematica

Prime[ Select[Range[2000], Apply[ Plus, IntegerDigits[ Prime[ # ]]] == Apply[ Plus, IntegerDigits[ Prime[ # + 1]]] & ]]
Prime[#]&/@(SequencePosition[Total[IntegerDigits[#]]&/@Prime[Range[2000]],{x_,x_}][[;;,1]]) (* Harvey P. Dale, Mar 27 2025 *)

PARI

upto(limit)={my(d=2, L=List()); forprime(p=3, nextprime(limit+1), my(s=sumdigits(p)); if(s==d, listput(L, precprime(p-1))); d=s); Vec(L) } \\ Harry J. Smith, Feb 22 2010

PARI

is_A066540(p)={my(n=nextprime(p+1)); (n-p)%18==0 & isprime(p) & A007953(p)==A007953(n)}  \\ M. F. Hasler, Oct 13 2012

Python

from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    p, hp, q, hq = 2, 2, 3, 3
    while True:
        if hp == hq: yield p
        p, q = q, nextprime(q)
        hp, hq = hq, sum(map(int, str(q)))
print(list(islice(agen(), 42))) # Michael S. Branicky, Feb 19 2024