A208325 Primes p such that all p-k!! are composite for 1<=k!!<p.

2, 23, 29, 41, 47, 83, 113, 163, 167, 173, 191, 223, 233, 251, 257, 263, 269, 293, 307, 337, 347, 353, 373, 383, 419, 461, 503, 587, 593, 599, 631, 659, 673, 683, 719, 761, 797, 839, 853, 881, 1009, 1013, 1049, 1091, 1129, 1163, 1187, 1217, 1259, 1283, 1289

Offset

0,1

Links

Table of n, a(n) for n=0..50.

Example

29 is in the sequence because :
29 - 0!! = 29 - 1 = 28;
29 - 1!! = 29 - 1 = 28;
29 - 2!! = 29 - 2 = 27;
29 - 3!! = 29 - 3 = 26;
29 - 4!! = 29 - 8 = 21;
29 - 5!! = 29 - 15 = 14 is the last composite because 6!! = 48 > 29.

Maple

with(numtheory): for n from 1 to 250 do:p:=ithprime(n):i:=0:for k from 0 to p while (doublefactorial(k)<p) do:x:=p - doublefactorial(k):if type(x, prime)=true then i:=1:else fi:od:if i=0 then printf(`%d, `, p):else fi:od:

Crossrefs

Cf. A064152, A006882.

Sequence in context: A235150 A114549 A235148 * A255564 A034843 A084373

Adjacent sequences: A208322 A208323 A208324 * A208326 A208327 A208328

Keyword

nonn,easy

Author

Michel Lagneau, Feb 25 2012

Status

approved