A287660 a(n) = least prime p such that the triple of consecutive primes (p, q, r) has the property that p + prime(n+2) = q + prime(n+1) = r + prime(n).

3, 7, 5, 7, 5, 7, 31, 29, 23, 19, 5, 7, 31, 47, 29, 23, 19, 5, 23, 19, 31, 359, 397, 5, 7, 5, 7, 113, 109, 31, 29, 139, 137, 23, 47, 19, 31, 47, 29, 139, 137, 7, 5, 509, 199, 463, 5, 7, 31, 29, 139, 331, 47, 47, 29, 23, 19, 5, 139, 773, 109, 5, 7, 113, 947, 241

Offset

2,1

Comments

The sequence is generalizable to M (rather than 3) conditions. For instance, with four equalities we obtain the following sequence: least prime p such that the 4-tuple of consecutive primes (p, q, r, t) has the property that p + prime(n+3) = q + prime(n+2) = r + prime(n+1) = t + prime(n). The corresponding sequence is 5, 7, 5, 7, 31, 29, 23, 19, 17, 7, ... for n = 3, 4, ...

Links

Table of n, a(n) for n=2..67.

Example

a(2) = 3 because the triple of consecutive primes (3, 5, 7) has the property that 3 + prime(2+2) = 5 + prime(2+1) = 7 + prime(2) = 10. For n = 2, p = 3 is unique.
a(3) = 7 because the triple of consecutive primes (7, 11, 13) has the property that 7 + prime(3+2) = 11 + prime(3+1) = 13 + prime(3) = 18. For n = 3, the other values of p are 13, 37, 67, 97, 103, 193, ... where p == 3 or 7 (mod 10).

Maple

nn:=100:
for i from 2 to nn do:
  p1:=ithprime(i):p2:=ithprime(i+1):p3:=ithprime(i+2):
  ii:=0:
    for j from 2 to nn while(ii=0)do:
      q1:=ithprime(j):q2:=ithprime(j+1):q3:=ithprime(j+2):
       if p1+q3=p2+q2 and p1+q3=p3+q1 and p2+q2=p3+q1
        then
        ii:=1: printf(`%d, `, q1):
        else
       fi:
    od:
od:

Crossrefs

Cf. A000040.

Sequence in context: A010624 A019638 A116535 * A122001 A161327 A151685

Adjacent sequences: A287657 A287658 A287659 * A287661 A287662 A287663

Keyword

nonn,easy

Author

Michel Lagneau, May 29 2017

Status

approved