A226803 -id:A226803 - cp's OEIS frontend

A165504 Primes p with a digits sum of p^2 equal to 43.

887, 1697, 1723, 1867, 1913, 2083, 2137, 2417, 2543, 2633, 2687, 2767, 2803, 2957, 3083, 3109, 3137, 3433, 3793, 3847, 3947, 4073, 4217, 4423, 4567, 4657, 4783, 4793, 4937, 5099, 5233, 5279, 5333, 5387, 5431, 5647, 5683, 5827, 6043, 6053, 6133, 6143

Offset: 1

Vincenzo Librandi, Sep 21 2009

			887 is in the sequence because 887^2=786769 and 7+8+6+7+6+9=43.
1723 is in the sequence because 1723^2=2968729 and 2+9+6+8+7+2+9=43.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. primes p where the digital sum of p^2 is equal to: A226803 (7), A165492 (13), A165493 (19), A165502 (31), A165503 (37), this sequence (43).

[p: p in PrimesUpTo(6150) | &+Intseq(p^2) eq 43]; // Vincenzo Librandi, Sep 12 2013

Select[Prime[Range[300]], Total[IntegerDigits[#^2]] == 43&] (* Vincenzo Librandi, Sep 12 2013 *)

{A000040(i) : A123157(i) = 43} [R. J. Mathar, Sep 29 2009]

More terms from R. J. Mathar, Sep 29 2009

A165503 Primes p with a digits sum of p^2 equal to 37.

Original entry on oeis.org

433, 613, 683, 773, 827, 863, 1063, 1117, 1187, 1223, 1567, 1583, 1657, 1693, 1783, 1907, 1997, 2017, 2087, 2141, 2143, 2161, 2267, 2357, 2393, 2467, 2557, 2593, 2609, 2663, 2719, 2753, 2789, 2843, 2879, 2897, 2969, 2971, 3023, 3041, 3061, 3167, 3187

Offset: 1

Vincenzo Librandi, Sep 21 2009

			433 is in the sequence because 433^2=187489 and 1+8+7+4+8+9=37.
1783 is in the sequence because 1783^2=3179089 and 3+1+7+9+0+8+9=37.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. primes p where the digital sum of p^2 is equal to: A226803 (7), A165492 (13), A165493 (19), A165502 (31), this sequence (37), A165504 (43).

[p: p in PrimesUpTo(6150) | &+Intseq(p^2) eq 37]; // Vincenzo Librandi, Sep 12 2013

Select[Prime[Range[500]], Total[IntegerDigits[#^2]]== 37&] (* Vincenzo Librandi, Sep 12 2013 *)

{A000040(i) : A123157(i) = 37} [R. J. Mathar, Sep 29 2009]

More terms from R. J. Mathar, Sep 29 2009

A229058 Primes p where the digital sum of p^2 is equal to 25.

Original entry on oeis.org

67, 113, 157, 193, 257, 283, 311, 337, 373, 409, 419, 463, 509, 599, 643, 653, 661, 743, 761, 769, 797, 1013, 1031, 1039, 1103, 1129, 1193, 1237, 1301, 1381, 1399, 1427, 1471, 1481, 1553, 1571, 1579, 1597, 1733, 1759, 1823, 1831, 1877, 2029, 2039, 2111, 2129

Offset: 1

Vincenzo Librandi, Sep 12 2013

nonn

From Bruno Berselli, Sep 12 2013: (Start)
Primes q such that the digital sum of q^2 is 1 < k < 50:
k  | q
---|------------
| 2, 11, 101;
| A226803;
| 3;
| A226802;
| A165492;
| A165459;
| A165493;
| 43, 97, 191, 227, 241, 317, 331, 353, ... ;
| this sequence;
| 163, 197, 233, 307, 359, 397, 431, 467, ... ;
| A165502;
| 167, 293, 383, 563, 607, 617, 733, 787, ... ;
| A165504;
| 313, 947, 983, 1303, 1483, 1609, 1663, ... ;
| A165504;
| 883, 937, 1367, 1637, 2213, 2447, 2683, ... ;
| 1667, 2383, 2437, 2617, 2963, 4219, 4457, ... . (End)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A165459, A165492, A165493, A165502-A165504, A226802, A226803.

[p: p in PrimesUpTo(2600) | &+Intseq(p^2) eq 25];

Select[Prime[Range[400]], Total[IntegerDigits[#^2]] == 25 &]

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

Original entry on oeis.org

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

Antonio Graciá Llorente, Dec 26 2013

A123157 sorted and duplicates removed.

Cf. A067180, A067523, A123157, A056991.

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

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

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).
2, 11, 101, ... (A062397);
5, 149, 1049, ... (A226803);
only 3;
19, 71, 179, 251, 449, 20249, 24499, 100549, ... (A226802);
7, 29, 47, 61, 79, 151, 349, 389, 461, 601, 1051, 1249, 1429, ... (A165492);
13, 23, 31, 41, 59, 103, 131, 139, 211, 229, 239, 347, 401, ... (A165459);
17, 37, 53, 73, 89, 107, 109, 127, 181, 199, 269, 271, 379, ... (A165493);
43, 97, 191, 227, 241, 317, 331, 353, 421, 439, 479, 569, 619, 641, ...;
67, 113, 157, 193, 257, 283, 311, 337, 373, 409, 419, 463, ... (A229058);
163, 197, 233, 307, 359, 397, 431, 467, 487, 523, 541, 577, 593, 631, ...;
83, 137, 173, 223, 263, 277, 281, 367, 443, 457, 547, 587, ... (A165502);
167, 293, 383, 563, 607, 617, 733, 787, 823, 859, 877, 941, 967, 977, ...;
433, 613, 683, 773, 827, 863, 1063, 1117, 1187, 1223, 1567, ... (A165503);
313, 947, 983, 1303, 1483, 1609, 1663, 1933, 1973, 1987, 2063, 2113, ...;
887, 1697, 1723, 1867, 1913, 2083, 2137, 2417, 2543, 2633, ... (A165504);
883, 937, 1367, 1637, 2213, 2447, 2683, 2791, 2917, 3313, 3583, 3833, ...;
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)

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

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A165504 Primes p with a digits sum of p^2 equal to 43.

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A165503 Primes p with a digits sum of p^2 equal to 37.

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A229058 Primes p where the digital sum of p^2 is equal to 25.

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Magma

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

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