A362065 Write the English name of a(n); sum the ranks of its letters in the alphabet; divide the sum by a(n); the result is an integer.

1, 2, 4, 16, 134

Offset: 1

Author

Eric Angelini and Mensanator, Apr 07 2023

Keywords

• base
• nonn
• fini
• full
• word

Comments

Is a(5) = 134 the last such term?

Indices of zeros in A226911; and conjectured finite, full based on an observation there. - Michael S. Branicky, Apr 07 2023

If a(6) exists, it is > 10^7. - Robert G. Wilson v, Apr 22 2023

There are no more terms because for any number k > 10^6, the sum of the ranks of the letters in the English name of k will be far less than k. - Erich Friedman, Nov 13 2024

Examples

			a(1) = 1 = ONE and O+N+E = 34 and 34/1 = 34;
a(2) = 2 = TWO and T+W+O = 58 and 58/2 = 29;
a(3) = 4 = FOUR and F+O+U+R = 60 and 60/4 = 15;
a(4) = 16 = SIXTEEN and S+I+X+T+E+E+N = 96 and 96/16 = 6; etc.
		

Crossrefs

Cf. A092320, A126259, A073327, A226911.

Programs

Mathematica

Position[Array[Mod[Total@ Flatten[ToCharacterCode[#] - 96 & /@ Characters@ StringDelete[IntegerName[#], Except@ LetterCharacter]], #] &, 10^4] , 0][[All, 1]] (* Michael De Vlieger, Apr 07 2023 *)