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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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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 * A071613 A262649 A202277

Adjacent sequences:  A007510 A007511 A007512 * A007514 A007515 A007516

KEYWORD

base,nonn,easy,nice,look

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

Terms beyond a(57) by R. J. Mathar, Dec 09 2009

STATUS

approved

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Last modified December 7 05:39 EST 2016. Contains 278841 sequences.