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A007513
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a(n) = initial prime of n consecutive primes such that first and last have same digit sum.
(Formerly M2186)
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2
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2, 523, 109, 79, 2, 13, 5, 127, 47, 17, 5, 127, 53, 17, 7, 67, 31, 37, 47, 37, 83, 11, 43, 19, 157, 2, 37, 5, 47, 5, 19, 67, 7, 29, 19, 53, 31, 73, 53, 29, 139, 13, 67, 83, 7, 47, 29, 17, 79, 7, 19, 37, 59, 43, 271, 19, 29, 181, 167, 59, 97, 5, 149, 7, 59, 337, 41, 53, 43, 127
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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J. R. Smart, A new function from a table of primes, J. Rec. Math., 7 (No. 4, 1974), 293-294.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
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EXAMPLE
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523 and 541 are first pair of consecutive primes with same sum of digits (10).
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MAPLE
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A007953 := proc(n) local d; add(d, d=convert(n, base, 10)) ; end proc: A007605 := proc(n) A007953(ithprime(n)) ; end proc: A007513 := proc(n) for i from 1 do if A007605(i) = A007605(i+n-1) then return ithprime(i) ; end if; end do ; end proc: seq(A007513(n), n=1..120) ; [From R. J. Mathar, Dec 09 2009]
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MATHEMATICA
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prms=Prime[Range[2000]]; First/@Table[First[Select[Partition[prms, n, 1], Total[IntegerDigits[First[#]]]==Total[IntegerDigits[Last[#]]]&]], {n, 75}] (* From Harvey P. Dale, May 20 2011 *)
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PROG
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(Haskell)
import Data.Function (on)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a007513 n = a000040_list !! (fromJust $ elemIndex 0 $
zipWith ((-) `on` a007953) a000040_list $ drop (n-1) a000040_list)
-- Reinhard Zumkeller, Aug 17 2011
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CROSSREFS
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Sequence in context: A182446 A218436 A080778 * A071613 A202277 A177836
Adjacent sequences: A007510 A007511 A007512 * A007514 A007515 A007516
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KEYWORD
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base,nonn,easy,nice
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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Terms beyond a(57) by R. J. Mathar, Dec 09 2009
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STATUS
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approved
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