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A138091 Numbers n such that n^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4+(n+5)^5+(n+6)^6+(n+7)^7+(n+8)^8+(n+9)^9+(n+10)^10+(n+11)^11+(n+12)^12+(n+13)^13 is a prime. 1
25, 43, 55, 109, 131, 379, 389, 587, 617, 649, 683, 697, 719, 971, 1013, 1279, 1291, 1727, 1735, 1823, 1853, 2005, 2059, 2087, 2167, 2395, 2399, 2561, 2647, 2783, 2957, 2983 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1618

MATHEMATICA

a={}; Do[If[PrimeQ[n^70+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4+(n+5)^5+(n+6)^6+(n+7)^7+(n+8)^8+(n+9)^9+(n+10)^10+(n+11)^11+(n+12)^12+(n+13)^13], AppendTo[a, n]], {n, 10^3*3}]; a

Select[Range[3000], PrimeQ[Total[Range[#, #+13]^Range[0, 13]]]&] (* Harvey P. Dale, Apr 25 2018 *)

PROG

(Python)

from sympy import isprime

A138091_list, m = [], [6227020800, 44068147200, 181142438400, 564307430400, 1475073815040, 3408641107200, 7182564530400, 14081919023520, 26048741640120, 45924510262992, 77755456075656, 127171611204708, 201851662963039, 312086923782438]

for n in range(1, 2*10**5+1):

....for i in range(13):

........m[i+1]+= m[i]

....if isprime(m[-1]):

........A138091_list.append(n) # Chai Wah Wu, Nov 06 2014

CROSSREFS

Sequence in context: A240758 A031331 A236838 * A105507 A015911 A188005

Adjacent sequences:  A138088 A138089 A138090 * A138092 A138093 A138094

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 06 2008

STATUS

approved

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Last modified February 22 05:17 EST 2019. Contains 320385 sequences. (Running on oeis4.)