A370362 Numbers k such that any two consecutive decimal digits of k^2 differ by 1 after arranging the digits in decreasing order.

0, 1, 2, 3, 18, 24, 66, 74, 152, 179, 3678, 3698, 4175, 4616, 5904, 5968, 6596, 7532, 8082, 8559, 9024, 10128, 10278, 11826, 12363, 12543, 12582, 13278, 13434, 13545, 13698, 14442, 14676, 14766, 15681, 15963, 16854, 17529, 17778, 18072, 19023, 19377, 19569, 19629

Offset

1,3

Comments

Numbers k such that k^2 is in A215014. There are 160 terms in this sequence.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..160

Example

18^2 = 324 consists of the consecutive digits 2, 3 and 4;
24^2 = 576 consists of the consecutive digits 5, 6 and 7;
66^2 = 4356 consists of the consecutive digits 3, 4, 5 and 6;
74^2 = 5476 consists of the consecutive digits 4, 5, 6 and 7.

Prog

(PARI) isconsecutive(m, {b=10})=my(v=vecsort(digits(m, b))); for(i=2, #v, if(v[i]!=1+v[i-1], return(0))); 1 \\ isconsecutive(k, b) == 1 if and only if any two consecutive digits of the base-n expansion of m differ by 1 after arranging the digits in decreasing order
a(n) = isconsecutive(n^2)
(Python)
from math import isqrt
from sympy.ntheory import digits
def afull(): return([i for i in range(isqrt(10**10)+1) if len(d:=sorted(str(i*i))) == ord(d[-1])-ord(d[0])+1 == len(set(d))])
print(afull()) # Michael S. Branicky, Feb 23 2024

Crossrefs

Cf. A215014, A370370. Supersequence of A156977.

The actual squares are given by A370610.

Sequence in context: A037317 A112664 A216890 * A047191 A096308 A073529

Adjacent sequences: A370359 A370360 A370361 * A370363 A370364 A370365

Keyword

nonn,base,fini,full

Author

Jianing Song, Feb 16 2024

Status

approved