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A054268 Sum of composite numbers between prime p and nextprime(p) is a repdigit. 10
3, 5, 109, 111111109, 259259257 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

No additional terms below 472882027.

LINKS

Table of n, a(n) for n=0..4.

Eric Weisstein's World of Mathematics, Repdigit

FORMULA

Numbers A000040(n) for n > 1 such that A001043(n)*(A001223(n)-1)/2 is in A010785. - Chai Wah Wu, Aug 12 2014

EXAMPLE

a(5) is ok since between 259259257 and nextprime 259259261 we get the sum 259259258 + 259259259 + 259259260 which yield repdigit 777777777.

MATHEMATICA

repQ[n_]:=Count[DigitCount[n], 0]==9; Select[Prime[Range[2, 14500000]], repQ[Total[Range[#+1, NextPrime[#]-1]]]&] (* Harvey P. Dale, Jan 29 2011 *)

PROG

(Python)

from sympy import prime

A054268 = [prime(n) for n in xrange(2, 10**5) if len(set(str(int((prime(n+1)-prime(n)-1)*(prime(n+1)+prime(n))/2)))) == 1]

# Chai Wah Wu, Aug 12 2014

CROSSREFS

Cf. A010785, A028987, A028988, A046933, A054264, A054265, A054266, A054267.

Sequence in context: A130187 A289488 A054266 * A153137 A105526 A070743

Adjacent sequences:  A054265 A054266 A054267 * A054269 A054270 A054271

KEYWORD

nonn,base,hard

AUTHOR

Patrick De Geest, Apr 15 2000

STATUS

approved

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Last modified January 20 10:38 EST 2018. Contains 297960 sequences.