A178823 - OEIS

%I #11 Mar 31 2012 13:22:29

%S 1,4,5,11,12,13,24,73,1103,1115,1117,1117,1117,1117,1117,1140,1144,

%T 1201,1217,1217,1323,1326,1340,1344,1374,1413,1413,1413,1413,1424,

%U 1441,1441,1480,1484

%N a(1) = 1, a(n+1) = least k >= a(n) such that the sum of the number of letters in the English name of all values in the sequence through a(n), excluding spaces and hyphens (A005589), is prime.

%e a(1) = 1 by definition.

%e a(2) = 4 because "one" plus "four" has 3 + 4 = 7 letters, with 7 prime.

%e a(3) = 5 because "one" plus "four" plus "five" gives 3 + 4 + 4 = 11, a prime.

%e a(4) = 11 because "one" plus "four" plus "five" plus "eleven" gives 3 + 4 + 4 + 6 = 17 is prime.

%e a(5) = 12 because "one" plus "four" plus "five" plus "eleven" plus "twelve" gives 3 + 4 + 4 + 6 + 6 = 23 is prime.

%e a(6) = 13 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" gives 3 + 4 + 4 + 6 + 6 + 8 = 31 is prime.

%e a(7) = 24 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 = 41 is prime.

%e a(8) = 73 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" plus "seventythree" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 + 12 = 53 is prime.

%e a(9) = 1103 because "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" plus "seventythree" plus "one thousand one hundred three" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 + 12 + 26 = 79 is prime.

%e a(10) = 1115 "one" plus "four" plus "five" plus "eleven" plus "twelve" plus "thirteen" plus "twentyfour" plus "seventythree" plus "one thousand one hundred three" plus "one thousand one hundred fifteen" gives 3 + 4 + 4 + 6 + 6 + 8 + 10 + 12 + 26 + 28 = 107 is prime.

%Y Cf. A006944 (ordinals), A052360, A052362-A052363, A005589, A134629, A133418, A016037

%K nonn,easy,word

%O 1,2

%A _Jonathan Vos Post_, Dec 26 2010

%E a(11)-a(34) from _Nathaniel Johnston_, Jan 04 2011