A176466 Smallest primes p which give a prime iterated by f(p,k) = 2 * p + prime(k+1) for at least three steps (k = 1, 2, ...).

2, 13, 5, 199, 2, 13, 251, 487, 61, 5, 113, 19, 2, 13, 157, 1621, 269, 23, 139, 557, 5, 37, 241, 5, 19, 587, 823, 41, 97, 5, 109, 13, 1151, 31, 1409, 53, 5, 1543, 67, 421, 5, 1039, 2, 13, 41, 359, 1697, 43, 101, 157

Offset

1,1

Comments

See comments and references of A176379

p, f(p,k) = 2 * p + prime(k+1), q = f(f(p,k)) = 4 * p + 3 * prime(k+1), r = 8 * p + 7 * prime(k+1)

p, f(p,k), q and r to be prime

List of (p,f(p,k),q):

(2,7,17,37) (13,31,67,139) (5,17,41,89) (199,409,829,1669) (2,17,47,107)

(13,43,103,223) (251,521,1061,2141) (487,997,2017,4057) (61,151,331,691) (5,41,113,257)

(113,263,563,1163) (19,79,199,439) (2,47,137,317) (13,73,193,433) (157,367,787,1627)

(1621,3301,6661,13381) (269,599,1259,2579) (23,113,293,653) (139,349,769,1609) (557,1187,2447,4967)

(5,89,257,593) (37,157,397,877) (241,571,1231,2551) (5,107,311,719) (19,139,379,859)

(587,1277,2657,5417) (823,1753,3613,7333) (41,191,491,1091) (97,307,727,1567) (5,137,401,929)

(109,349,829,1789) (13,163,463,1063) (1151,2441,5021,10181) (31,211,571,1291) (1409,2969,6089,12329)

(53,263,683,1523) (5,173,509,1181) (1543,3253,6673,13513) (67,307,787,1747) (421,1021,2221,4621)

(5,191,563,1307) (1039,2269,4729,9649) (2,197,587,1367) (13,223,643,1483) (41,281,761,1721)

(359,929,2069,4349) (1697,3617,7457,15137) (43,313,853,1933) (101,431,1091,2411) (157,547,1327,2887)

Links

Table of n, a(n) for n=1..50.

Example

k=1: p=2, f(2,1) = 2 * 2 + prime(2) = 7, q = 4 * 2 + 3 * 3 = 17, r = 8 * 2 + 7 * 3 = 37, 2 is first term
k=2: p=13, f(13,2) = 2 * 13 + prime(3) = 31, q = 4 * 13 + 3 * 5 = 67, r = 8 * 13 + 7 * 5 = 139, 2 is 2nd term

Crossrefs

A000040, A005602, A059761, A059762, A110024 , A176379

Sequence in context: A268722 A213828 A324003 * A128155 A211366 A158088

Adjacent sequences: A176463 A176464 A176465 * A176467 A176468 A176469

Keyword

base,nonn,uned

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 18 2010

Status

approved