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

1,1

Comments

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

G. L. Honaker, Jr. and C. Caldwell, Prime Curios!

Example

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

Mathematica

Prime[ Select[Range[2000], Apply[ Plus, IntegerDigits[ Prime[ # ]]] == Apply[ Plus, IntegerDigits[ Prime[ # + 1]]] & ]]

Prog

(PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) }
{ n=0; d=2; for (m=2, 10^10, s=SumD(prime(m)); if (s==d, write("b066540.txt", n++, " ", prime(m-1)); if (n==1000, return) ); d=s ) }  \\ 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

Crossrefs

Subsequence of A117838. A069567 is a subsequence.

Cf. A007513, A007953, A209396, A210629.

Sequence in context: A095651 A117838 A031936 * A209875 A080912 A183830

Adjacent sequences: A066537 A066538 A066539 * A066541 A066542 A066543

Keyword

base,easy,nonn

Author

Jason Earls, Jan 06 2002

Status

approved