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

%I A066540 #50 Mar 27 2025 17:05:14
%S A066540 523,1069,1259,1759,1913,2503,3803,4159,4373,4423,4463,4603,4703,4733,
%T A066540 5059,5209,6229,6529,6619,7159,7433,7459,8191,9109,9749,9949,10691,
%U A066540 10753,12619,12763,12923,13763,14033,14107,14303,14369,15859,15973,16529,16673,16903,17239
%N A066540 The first of two consecutive primes with equal digital sums.
%C A066540 The difference between the two primes of the pair is a multiple of 18. - _Antonio Roldán_, Mar 13 2012
%H A066540 Harry J. Smith, <a href="/A066540/b066540.txt">Table of n, a(n) for n = 1..1000</a>
%H A066540 G. L. Honaker, Jr. and C. Caldwell, <a href="https://t5k.org/curios/page.php?short=523">Prime Curios!</a>
%e A066540 a(1) = 523 because both it and the next prime, 541, have a digital sum of 10.
%t A066540 Prime[ Select[Range[2000], Apply[ Plus, IntegerDigits[ Prime[ # ]]] == Apply[ Plus, IntegerDigits[ Prime[ # + 1]]] & ]]
%t A066540 Prime[#]&/@(SequencePosition[Total[IntegerDigits[#]]&/@Prime[Range[2000]],{x_,x_}][[;;,1]]) (* _Harvey P. Dale_, Mar 27 2025 *)
%o A066540 (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
%o A066540 (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 A066540 (Python)
%o A066540 from sympy import nextprime
%o A066540 from itertools import islice
%o A066540 def agen(): # generator of terms
%o A066540     p, hp, q, hq = 2, 2, 3, 3
%o A066540     while True:
%o A066540         if hp == hq: yield p
%o A066540         p, q = q, nextprime(q)
%o A066540         hp, hq = hq, sum(map(int, str(q)))
%o A066540 print(list(islice(agen(), 42))) # _Michael S. Branicky_, Feb 19 2024
%Y A066540 Subsequence of A117838. A069567 is a subsequence.
%Y A066540 Cf. A007513, A007953, A209396, A210629.
%K A066540 base,easy,nonn
%O A066540 1,1
%A A066540 _Jason Earls_, Jan 06 2002