cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A226803 Primes p where the digital sum of p^2 is equal to 7.

Original entry on oeis.org

5, 149, 1049
Offset: 1

Views

Author

Vincenzo Librandi, Jun 24 2013

Keywords

Comments

No more terms below 10^9. - Michel Marcus, Nov 02 2013
No more terms below 10^20. - Hiroaki Yamanouchi, Sep 23 2014

Examples

			5 is in the sequence because 5^2 = 25 and 2 + 5 = 7.
149 is in the sequence because 149^2 = 22201 and 2 + 2 + 2 + 0 + 1 = 7.

Crossrefs

Subsequence of A215614.
Cf. A226802, A165492, A165459, A165493.

Programs

  • Magma
    [p: p in PrimesUpTo(6*10^6) | &+Intseq(p^2) eq 7];
  • Mathematica
    Select[Prime[Range[10000]], Total[IntegerDigits[#^2]] == 7 &]
  • PARI
    lista(nn) = {forprime(p=2, nn, if (sumdigits(p^2)==7, print1(p, ", ")););} \\ Michel Marcus, Nov 02 2013

Extensions

Keywords fini,full, since unproven, removed by Max Alekseyev, Jun 20 2025

A226802 Primes p where the digital sum of p^2 is equal to 10.

Original entry on oeis.org

19, 71, 179, 251, 449, 20249, 24499, 100549
Offset: 1

Views

Author

Vincenzo Librandi, Jun 24 2013

Keywords

Comments

The next term is > 24154957 (if it exists). - R. J. Mathar, Jul 05 2013
No more terms below 10^12. - Hiroaki Yamanouchi, Sep 23 2014.
No additional terms < 10^15. - Chai Wah Wu, Nov 15 2015
No other terms below 10^50. The sequence is likely finite and complete. - Max Alekseyev, Jun 13 2025

Examples

			19 is in the sequence because 19^2=361 and 3+6+1=10.
71 is in the sequence because 71^2=5041 and 5+0+4+1=10.

Crossrefs

Cf. A123157, A165492, A165459, A165493. Subset of A135027.

Programs

  • Magma
    [p: p in PrimesUpTo(5*10^6) | &+Intseq(p^2) eq 10];
  • Maple
    select(p -> isprime(p) and convert(convert(p^2,base,10),`+`)=10, [seq(2*k+1,k=1..100000)]); # Robert Israel, Sep 23 2014
  • Mathematica
    Select[Prime[Range[70000]], Total[IntegerDigits[#^2]]== 10&]

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

Views

Author

Vincenzo Librandi, Sep 12 2013

Keywords

Comments

From Bruno Berselli, Sep 12 2013: (Start)
Primes q such that the digital sum of q^2 is 1 < k < 50:
k | q
---|------------
4 | 2, 11, 101;
7 | A226803;
9 | 3;
10 | A226802;
13 | A165492;
16 | A165459;
19 | A165493;
22 | 43, 97, 191, 227, 241, 317, 331, 353, ... ;
25 | this sequence;
28 | 163, 197, 233, 307, 359, 397, 431, 467, ... ;
31 | A165502;
34 | 167, 293, 383, 563, 607, 617, 733, 787, ... ;
37 | A165504;
40 | 313, 947, 983, 1303, 1483, 1609, 1663, ... ;
43 | A165504;
46 | 883, 937, 1367, 1637, 2213, 2447, 2683, ... ;
49 | 1667, 2383, 2437, 2617, 2963, 4219, 4457, ... . (End)

Links

Crossrefs

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

Programs

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

Views

Author

Antonio Graciá Llorente, Dec 26 2013

Keywords

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
Showing 1-4 of 4 results.

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