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%I #45 Feb 19 2024 06:34:52
%S 523,1069,1259,1759,1913,2503,3803,4159,4373,4423,4463,4603,4703,4733,
%T 5059,5209,6229,6529,6619,7159,7433,7459,8191,9109,9749,9949,10691,
%U 10753,12619,12763,12923,13763,14033,14107,14303,14369,15859,15973,16529,16673,16903,17239
%N The first of two consecutive primes with equal digital sums.
%C The difference between the two primes of the pair is a multiple of 18. - _Antonio Roldán_, Mar 13 2012
%H Harry J. Smith, <a href="/A066540/b066540.txt">Table of n, a(n) for n = 1..1000</a>
%H G. L. Honaker, Jr. and C. Caldwell, <a href="https://t5k.org/curios/page.php?short=523">Prime Curios!</a>
%e a(1) = 523 because both it and the next prime, 541, have a digital sum of 10.
%t Prime[ Select[Range[2000], Apply[ Plus, IntegerDigits[ Prime[ # ]]] == Apply[ Plus, IntegerDigits[ Prime[ # + 1]]] & ]]
%o (PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) }
%o { 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
%o (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
%o (Python)
%o from sympy import nextprime
%o from itertools import islice
%o def agen(): # generator of terms
%o p, hp, q, hq = 2, 2, 3, 3
%o while True:
%o if hp == hq: yield p
%o p, q = q, nextprime(q)
%o hp, hq = hq, sum(map(int, str(q)))
%o print(list(islice(agen(), 42))) # _Michael S. Branicky_, Feb 19 2024
%Y Subsequence of A117838. A069567 is a subsequence.
%Y Cf. A007513, A007953, A209396, A210629.
%K base,easy,nonn
%O 1,1
%A _Jason Earls_, Jan 06 2002
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