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

1,3

Comments

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

Links

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

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) = 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

Crossrefs

Cf. A215014, A370370. Supersequence of A036745.

The square roots are given by A370362.

Sequence in context: A029734 A085065 A068708 * A367451 A063248 A027522

Adjacent sequences: A370607 A370608 A370609 * A370611 A370612 A370613

Keyword

nonn,base,fini,full

Author

Jianing Song, Feb 23 2024

Status

approved