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A234429 Numbers which are the digital sum of the square of some prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A123157 sorted and duplicates removed.

LINKS

Table of n, a(n) for n=1..54.

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)

PROG

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

CROSSREFS

Cf. A067180, A067523, A123157, A056991.

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

Sequence in context: A010415 A010442 A055047 * A291201 A310940 A153001

Adjacent sequences:  A234426 A234427 A234428 * A234430 A234431 A234432

KEYWORD

nonn,base,more

AUTHOR

Antonio GraciĆ” Llorente, Dec 26 2013

EXTENSIONS

a(36) from Michel Marcus, Jan 08 2014

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

STATUS

approved

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Last modified February 22 09:43 EST 2019. Contains 320390 sequences. (Running on oeis4.)