A007513 a(n) = initial prime of n consecutive primes such that first and last have same digit sum. (Formerly M2186)

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

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

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

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