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

4, 7, 9, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178

Offset: 1

Author

Antonio Graciá Llorente, Dec 26 2013

Keywords

• nonn
• base

Comments

A123157 sorted and duplicates removed.

Crossrefs

Cf. A067180, A067523, A123157, A056991.

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

Programs

PARI

terms(nn) = {v = []; forprime (p = 1, nn, v = concat(v, sumdigits(p^2));); vecsort(v,,8);} \\ Michel Marcus, Jan 08 2014

Formula

From Robert G. Wilson v, Sep 28 2014: (Start)

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).

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

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

9: only 3;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

... Also see A229058. (End)

Conjectures from Chai Wah Wu, Apr 16 2025: (Start)

a(n) = 2*a(n-1) - a(n-2) for n > 5.

G.f.: x*(2*x^4 - x^3 - x^2 - x + 4)/(x - 1)^2. (End)

Extensions

a(36) from Michel Marcus, Jan 08 2014

a(37)-a(54) from Robert G. Wilson v, Sep 28 2014

More terms from Giovanni Resta, Aug 15 2019