A208325
Primes p such that all p-k!! are composite for 1<=k!!
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
Examples
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.
Programs
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Maple
with(numtheory): for n from 1 to 250 do:p:=ithprime(n):i:=0:for k from 0 to p while (doublefactorial(k)