A152147 Irregular triangle in which row n lists k > 0 such that the sum of digits of k^n equals k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 9, 1, 8, 17, 18, 26, 27, 1, 7, 22, 25, 28, 36, 1, 28, 35, 36, 46, 1, 18, 45, 54, 64, 1, 18, 27, 31, 34, 43, 53, 58, 68, 1, 46, 54, 63, 1, 54, 71, 81, 1, 82, 85, 94, 97, 106, 117, 1, 98, 107, 108, 1, 108, 1, 20, 40, 86, 103, 104, 106, 107, 126, 134, 135

Offset

1,2

Comments

Each row begins with 1 and has length A046019(n).

Links

T. D. Noe, Rows n = 1..1000 of triangle, flattened

V. Oxman and M. Stupel, A number whose square root is the sum of its digits, The Mathematical Gazette 108 (573) (2024), 513-514.

Example

1, 2, 3, 4, 5, 6, 7, 8, 9;
1, 9;
1, 8, 17, 18, 26, 27;              (A046459, with 0)
1, 7, 22, 25, 28, 36;              (A055575    "   )
1, 28, 35, 36, 46;                 (A055576    "   )
1, 18, 45, 54, 64;                 (A055577    "   )
1, 18, 27, 31, 34, 43, 53, 58, 68; (A226971    "   )
1, 46, 54, 63;
1, 54, 71, 81;
1, 82, 85, 94, 97, 106, 117;
1, 98, 107, 108;
1, 108;
1, 20, 40, 86, 103, 104, 106, 107, 126, 134, 135, 146;
1, 91, 118, 127, 135, 154; etc.

Prog

(Python)
def ok(k, r): return sum(map(int, str(k**r))) == k
def agen(rows, startrow=1, withzero=0):
  for r in range(startrow, rows + startrow):
    d, lim = 1, 1
    while lim < r*9*d: d, lim = d+1, lim*10
    yield from [k for k in range(1-withzero, lim+1) if ok(k, r)]
print([an for an in agen(13)]) # Michael S. Branicky, May 23 2021
(PARI) M152147=Map(); {A152147(n, k)=if(k<2, k, mapisdefined(M152147, [n, k], &k), k, !mapisdefined(M152147, [n, 0]), my(L=(n+1)*(5+log(n+1)*3), t=A152147(n, k-1)); until(t++>L|| sumdigits(t^n)==t, ); mapput(M152147, [n, if(t>L, t=0, k)], t); t)} \\ M. F. Hasler, Jun 12 2026

Crossrefs

Cf. A046000, A046017, A046471, A133509.

Sequence in context: A113009 A068064 A376770 * A333830 A067032 A052500

Adjacent sequences: A152144 A152145 A152146 * A152148 A152149 A152150

Keyword

base,tabf,nonn

Author

T. D. Noe, Nov 26 2008

Status

approved