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A234429 Numbers which are the digital sum of the square of some prime. 1

%I #60 Aug 15 2019 12:40:23

%S 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 73,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,127,

%U 130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175,178

%N Numbers which are the digital sum of the square of some prime.

%C A123157 sorted and duplicates removed.

%F From _Robert G. Wilson v_, Sep 28 2014: (Start)

%F 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 4: 2, 11, 101, ... (A062397);

%F 7: 5, 149, 1049, ... (A226803);

%F 9: only 3;

%F 10: 19, 71, 179, 251, 449, 20249, 24499, 100549, ... (A226802);

%F 13: 7, 29, 47, 61, 79, 151, 349, 389, 461, 601, 1051, 1249, 1429, ... (A165492);

%F 16: 13, 23, 31, 41, 59, 103, 131, 139, 211, 229, 239, 347, 401, ... (A165459);

%F 19: 17, 37, 53, 73, 89, 107, 109, 127, 181, 199, 269, 271, 379, ... (A165493);

%F 22: 43, 97, 191, 227, 241, 317, 331, 353, 421, 439, 479, 569, 619, 641, ...;

%F 25: 67, 113, 157, 193, 257, 283, 311, 337, 373, 409, 419, 463, ... (A229058);

%F 28: 163, 197, 233, 307, 359, 397, 431, 467, 487, 523, 541, 577, 593, 631, ...;

%F 31: 83, 137, 173, 223, 263, 277, 281, 367, 443, 457, 547, 587, ... (A165502);

%F 34: 167, 293, 383, 563, 607, 617, 733, 787, 823, 859, 877, 941, 967, 977, ...;

%F 37: 433, 613, 683, 773, 827, 863, 1063, 1117, 1187, 1223, 1567, ... (A165503);

%F 40: 313, 947, 983, 1303, 1483, 1609, 1663, 1933, 1973, 1987, 2063, 2113, ...;

%F 43: 887, 1697, 1723, 1867, 1913, 2083, 2137, 2417, 2543, 2633, ... (A165504);

%F 46: 883, 937, 1367, 1637, 2213, 2447, 2683, 2791, 2917, 3313, 3583, 3833, ...;

%F 49: 1667, 2383, 2437, 2617, 2963, 4219, 4457, 5087, 5281, 6113, 6163, ...;

%F ... Also see A229058. (End)

%o (PARI) terms(nn) = {v = []; forprime (p = 1, nn, v = concat(v, sumdigits(p^2));); vecsort(v,,8);} \\ _Michel Marcus_, Jan 08 2014

%Y Cf. A067180, A067523, A123157, A056991.

%Y Cf. A062397, A226803, A226802, A165492, A165459 A165493, A229058, A165502, A165503, A165504.

%K nonn,base

%O 1,1

%A _Antonio GraciĆ” Llorente_, Dec 26 2013

%E a(36) from _Michel Marcus_, Jan 08 2014

%E a(37)-a(54) from _Robert G. Wilson v_, Sep 28 2014

%E More terms from _Giovanni Resta_, Aug 15 2019

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)