A138091 Numbers k such that Sum_{j=0..13} (k + j)^j is a prime.

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, 3011, 3127, 3233, 3245, 3323, 3335, 3433, 3631, 3763, 3827, 3931, 3995, 4211, 4345, 4367

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 06 2008

Keywords

• nonn

Links

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

Programs

Maple

q:= n-> isprime(add((n+j)^j, j=0..13)):
select(q, [$1..5000])[];  # Alois P. Heinz, Nov 22 2024

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 *)

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