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A007513 a(n) = initial prime of n consecutive primes such that first and last have same digit sum.
(Formerly M2186)
2
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)
OFFSET
1,1
REFERENCES
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).
LINKS
J. R. Smart, A new function from a table of primes, J. Recreational Mathematics 7.4 (1974), 293-294. (Annotated scanned copy)
EXAMPLE
523 and 541 are first pair of consecutive primes with same sum of digits (10).
MAPLE
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) ; # R. J. Mathar, Dec 09 2009
MATHEMATICA
prms=Prime[Range[2000]]; First/@Table[First[Select[Partition[prms, n, 1], Total[ IntegerDigits[ First[#]]]==Total[IntegerDigits[Last[#]]]&]], {n, 75}] (* Harvey P. Dale, May 20 2011 *)
PROG
(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
CROSSREFS
Sequence in context: A182446 A218436 A080778 * A352852 A283756 A352803
KEYWORD
base,nonn,easy,nice,look
AUTHOR
EXTENSIONS
Terms beyond a(57) by R. J. Mathar, Dec 09 2009
STATUS
approved

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Last modified May 18 15:59 EDT 2024. Contains 372664 sequences. (Running on oeis4.)