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A340868 Numbers k such that prime(k)^prime(k+1) == prime(k+3) (mod prime(k+2)). 2
15, 52, 701, 26017, 579994, 1131833 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For prime(k)^prime(k+1) == prime(k+2) (mod prime(k+3)), the first two examples are k = 942 and k = 4658911.

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

Primes number 52 to 55 are 239, 241, 251, 257, and 239^241 == 257 == 6 (mod 251), so 52 is in the sequence.

MAPLE

q:= 2: r:= 3: s:= 5: R:= NULL: count:= 0:

for k from 1 while count < 6 do

  p:= q; q:= r; r:= s; s:= nextprime(s);

  if p &^ q - s mod r = 0 then count:= count+1; R:= R, k fi

od:

R;

PROG

(Python)

from sympy import nextprime

k, p, q, r, s, A340868_list = 1, 2, 3, 5, 7, []

while k < 10**7:

    if pow(p, q, r) == s % r:

        A340868_list.append(k)

    k, p, q, r, s = k+1, q, r, s, nextprime(s) # Chai Wah Wu, Jan 25 2021

CROSSREFS

Cf. A340876.

Sequence in context: A332394 A220156 A333617 * A194454 A219384 A198955

Adjacent sequences:  A340865 A340866 A340867 * A340869 A340870 A340871

KEYWORD

nonn,more

AUTHOR

J. M. Bergot and Robert Israel, Jan 24 2021

STATUS

approved

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Last modified July 24 03:29 EDT 2021. Contains 346273 sequences. (Running on oeis4.)