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

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

Author

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

Keywords

• base
• nonn
• easy
• nice
• look

Examples

			523 and 541 are first pair of consecutive primes with same sum of digits (10).
		

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)

Programs

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

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 *)

Extensions

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