Wager Mage
Photo: Rodolfo Clix
The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ... (OEIS A007770). These are also the numbers whose 2-recurring digital invariant sequences have period 1.
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Read More »Let the sum of the squares of the digits of a positive integer be represented by . In a similar way, let the sum of the squares of the digits of be represented by , and so on. Iterating this sum-of-squared-digits map always eventually reaches one of the 10 numbers 0, 1, 4, 16, 20, 37, 42, 58, 89, or 145 (OEIS A039943; Porges 1945). If for some , then the original integer is said to be happy. For example, starting with 7 gives the sequence 7, 49, 97, 130, 10, 1, so 7 is a happy number. The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ... (OEIS A007770). These are also the numbers whose 2-recurring digital invariant sequences have period 1. The numbers of iterations required for these to reach 1 are 0, 5, 1, 2, 4, 3, 3, 2, 3, 4, 4, 2, 5, ... (OEIS A090425). The numbers of happy numbers less than or equal to 1, , , ... are given by 1, 3, 20, 143, 1442, 14377, 143071, ... (OEIS A068571). The first few consecutive happy numbers have , 129, 192, 262, 301, 319, 367, 391, ... (OEIS A035502). Similarly, the first few happy triplets start with 1880, 4780, 4870, 7480, 7839, ... (OEIS A072494). The first few happy primes are 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, ... (OEIS A035497). Once it is known whether a number is happy (or not), then any number in the sequence , , , ... will also be happy (or not). A number that is not happy is called unhappy. Unhappy numbers have eventually periodic sequences of which never reach 1. Any permutation of the digits of an unhappy or happy number must also be unhappy or happy. This follows from the fact that addition is commutative.
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Read More »To make your man happy emotionally, you have to be attentive to his needs and to know when to give him space. To make your man happy sexually, you have to want to try new things and to be bold and adventurous. But the most important part is that you are feeling happy while you're pleasing your man.
This article was co-authored by Alysha Jeney, MA, LMFT . Alysha Jeney is a Licensed Relationship Therapist, the Owner of Modern Love Counseling, and the Co-Founder of The Modern Love Box. She specializes in relationship therapy, intimacy building, and existential exploration. Alysha holds a BA in Psychology from The Metropolitan State University of Denver and an MA in Marriage and Family Therapy/Counseling from Regis University. She has been featured in publications such as The Washington Post and The Huffington Post. This article has been viewed 933,074 times.
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