cp's OEIS Frontend

A234429 Numbers which are the digital sum of the square of some prime.

%I A234429 #63 Apr 17 2025 09:52:10
%S A234429 4,7,9,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,
%T A234429 73,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,127,
%U A234429 130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175,178
%N A234429 Numbers which are the digital sum of the square of some prime.
%C A234429 A123157 sorted and duplicates removed.
%F A234429 From _Robert G. Wilson v_, Sep 28 2014: (Start)
%F A234429 Except for 3, all primes are congruent to +-1 (mod 3). Therefore, (3n +- 1)^2 = 9n^2 +- 6n + 1 which is congruent to 1 (mod 3).
%F A234429 4: 2, 11, 101, ... (A062397);
%F A234429 7: 5, 149, 1049, ... (A226803);
%F A234429 9: only 3;
%F A234429 10: 19, 71, 179, 251, 449, 20249, 24499, 100549, ... (A226802);
%F A234429 13: 7, 29, 47, 61, 79, 151, 349, 389, 461, 601, 1051, 1249, 1429, ... (A165492);
%F A234429 16: 13, 23, 31, 41, 59, 103, 131, 139, 211, 229, 239, 347, 401, ... (A165459);
%F A234429 19: 17, 37, 53, 73, 89, 107, 109, 127, 181, 199, 269, 271, 379, ... (A165493);
%F A234429 22: 43, 97, 191, 227, 241, 317, 331, 353, 421, 439, 479, 569, 619, 641, ...;
%F A234429 25: 67, 113, 157, 193, 257, 283, 311, 337, 373, 409, 419, 463, ... (A229058);
%F A234429 28: 163, 197, 233, 307, 359, 397, 431, 467, 487, 523, 541, 577, 593, 631, ...;
%F A234429 31: 83, 137, 173, 223, 263, 277, 281, 367, 443, 457, 547, 587, ... (A165502);
%F A234429 34: 167, 293, 383, 563, 607, 617, 733, 787, 823, 859, 877, 941, 967, 977, ...;
%F A234429 37: 433, 613, 683, 773, 827, 863, 1063, 1117, 1187, 1223, 1567, ... (A165503);
%F A234429 40: 313, 947, 983, 1303, 1483, 1609, 1663, 1933, 1973, 1987, 2063, 2113, ...;
%F A234429 43: 887, 1697, 1723, 1867, 1913, 2083, 2137, 2417, 2543, 2633, ... (A165504);
%F A234429 46: 883, 937, 1367, 1637, 2213, 2447, 2683, 2791, 2917, 3313, 3583, 3833, ...;
%F A234429 49: 1667, 2383, 2437, 2617, 2963, 4219, 4457, 5087, 5281, 6113, 6163, ...;
%F A234429 ...  Also see A229058. (End)
%F A234429 Conjectures from _Chai Wah Wu_, Apr 16 2025: (Start)
%F A234429 a(n) = 2*a(n-1) - a(n-2) for n > 5.
%F A234429 G.f.: x*(2*x^4 - x^3 - x^2 - x + 4)/(x - 1)^2. (End)
%o A234429 (PARI) terms(nn) = {v = []; forprime (p = 1, nn, v = concat(v, sumdigits(p^2));); vecsort(v,,8);} \\ _Michel Marcus_, Jan 08 2014
%Y A234429 Cf. A067180, A067523, A123157, A056991.
%Y A234429 Cf. A062397, A226803, A226802, A165492, A165459  A165493, A229058, A165502, A165503, A165504.
%K A234429 nonn,base
%O A234429 1,1
%A A234429 _Antonio Graciá Llorente_, Dec 26 2013
%E A234429 a(36) from _Michel Marcus_, Jan 08 2014
%E A234429 a(37)-a(54) from _Robert G. Wilson v_, Sep 28 2014
%E A234429 More terms from _Giovanni Resta_, Aug 15 2019