A354521 a(n) is the position of the first letter in the US English name of n that can also be found in the English name of n+1.

2, 1, 1, 3, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Ray G. Opao, Aug 16 2022

Keywords

• nonn
• easy
• word

Comments

Spaces and punctuation are ignored when determining the position of the letter.

a(n) is well-defined as n and n+1 always share a letter (see formulas). - Michael S. Branicky, Aug 20 2022

Examples

			For n = 4, a(4) = 1 since the 1st letter of 'four' can also be found in 'five'.
For n = 59, a(59) = 2 since the 2nd letter of 'fifty-nine' can be found in 'sixty'.
		

Programs

Python

from num2words import num2words as n2w
def a(i):
    w1 = n2w(i).replace(' ','').replace('-','')
    w2 = n2w(i+1).replace(' ','').replace('-','')
    for j in range(len(w1)):
        if w1[j] in w2:
            return j+1

Formula

For n > 1000, a(n) = 1 unless n = b + 1000^e - 1 (for e >= 1, 1 <= b <= 999) in which case a(n) = a(b). Subsequently, 1 <= a(n) <= 3. - Michael S. Branicky, Aug 20 2022