A370610 Squares such that any two consecutive decimal digits differ by 1 after arranging the digits in decreasing order.

0, 1, 4, 9, 324, 576, 4356, 5476, 23104, 32041, 13527684, 13675204, 17430625, 21307456, 34857216, 35617024, 43507216, 56731024, 65318724, 73256481, 81432576, 102576384, 105637284, 139854276, 152843769, 157326849, 158306724, 176305284, 180472356, 183467025, 187635204

Offset: 1

Author

Jianing Song, Feb 23 2024

Keywords

• nonn
• base
• fini
• full

Comments

Squares in A215014. There are 160 terms in this sequence.

Links

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

Crossrefs

Cf. A215014, A370370. Supersequence of A036745.

The square roots are given by A370362.

Programs

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) = issquare(n) && isconsecutive(n)

Python

from math import isqrt
from sympy.ntheory import digits
def afull(): return([i*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