A296521 Anagrasum integers: integers N that exactly reproduce their set of digits when we form the set of sums of pairs of adjacent digits.

190, 1091, 1459, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 2091, 3091, 4091, 5091, 6091, 7091, 7189, 8091, 9091, 9180, 9541, 9817, 10091, 10819, 11082, 12073, 13064, 14055, 15046, 16037, 17028, 18019, 19000, 19001, 19002, 19003, 19004, 19005, 19006, 19007, 19008, 19009, 20091, 20819, 28011, 30091

Offset

1,1

Comments

The sequence is infinite, since a term ending in zero can be extended with as many zeros as needed. The name "anagrasum numbers" comes from "anagram by sum". The "anagraprod numbers" are A296451.

Links

Georges Brougnard, Table of n, a(n) for n = 1..421

Example

190 reproduces the digits 1, 9 and 0 (in a different order) when the sums 1+9=10 and 9+0=9 are taken. The same with 12073, for instance, which reproduces the digits 1, 2, 0, 7 and 3 when the sums 1+2=3, 2+0=2, 0+7=7 and 7+3=10 are formed.

Mathematica

Select[Range[32000], Function[d, Sort@ Flatten@ Map[IntegerDigits[Total@ #] &, Partition[d, 2, 1]] == Sort@ d]@ IntegerDigits@ # &] (* Michael De Vlieger, Dec 14 2017 *)

Prog

(Python)
def ok(n):
    s = str(n)
    d = list(map(int, s))
    sums = [d[i]+d[i+1] for i in range(len(s)-1)]
    return sorted(s) == sorted("".join(str(t) for t in sums))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Nov 27 2024

Crossrefs

Cf. A296451, A297627.

Sequence in context: A248995 A258725 A232387 * A223462 A184192 A263523

Adjacent sequences: A296518 A296519 A296520 * A296522 A296523 A296524

Keyword

base,nonn

Author

Eric Angelini and Georges Brougnard, Dec 14 2017

Status

approved