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A066540 The first of two consecutive primes with equal digital sums. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The difference between the two primes of the pair is a multiple of 18. - Antonio Roldán, Mar 13 2012
LINKS
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.
Sequence in context: A095651 A117838 A031936 * A209875 A080912 A183830
KEYWORD
base,easy,nonn
AUTHOR
Jason Earls, Jan 06 2002
STATUS
approved

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)