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A243097 Digit sums of the nontrivial reversal numbers (numbers which are integer multiples of their reversal), excluding palindromes and multiples of 10.

18, 18, 27, 27, 36, 36, 45, 45, 36, 54, 36, 54, 36, 63, 36, 63, 36, 54, 72, 36, 54, 72, 36, 54, 81, 36, 54, 81, 36, 54, 54, 72, 90, 36, 54, 54, 72, 90, 36, 63, 54, 72, 99, 36, 63, 54, 72, 99, 36, 54, 72, 54, 72, 72, 90, 108, 36, 54, 72, 54, 72, 72, 90, 108

Offset: 1

Sam Mathers, Aug 18 2014

			a(1)=digit sum of 8712=8+7+1+2=18, a(3)=digit sum of 87912=8+7+9+1+2=27.

Cf. A007953 (digit sum), A031877 (union of A222814 and A222815).

A243097 = []
for n in range(1,10**7):
    if n % 10:
        s1 = str(n)
        s2 = s1[::-1]
        if s1 != s2 and not n % int(s2):
            A243097.append(sum(int(d) for d in s1))
# Chai Wah Wu, Sep 05 2014

a(n) = 9(d-2p-b) where d is the number of digits in the reversal number, p is the number of repeating units of either 8712 or 9801 (they can be split in the middle of the sequence as long as all 4 numbers appear in the correct order), and b is the number of digits separating two complete "units" (must appear between two complete units and not in between 1 incomplete unit).

a(n) = A007953(A031877(n)).

More terms from Michel Marcus, Aug 25 2014

A242757 Partial sums of the number of integers between successive twin prime pairs.

Original entry on oeis.org

0, 3, 6, 15, 24, 39, 48, 75, 78, 105, 114, 141, 150, 153, 180, 189, 216, 225, 252, 285, 354, 363, 390, 447, 492, 519, 534, 555, 570, 717, 726, 729, 756, 777, 912, 921, 936, 945, 972, 1029, 1104, 1149, 1158, 1167

Offset: 1

Sam Mathers, Aug 16 2014

nonn

a(n) is the partial sum of the number of integers separating each successive pair of twin prime numbers less than and up to the n-th pair of twin primes.

			For n=4, a(4)=15 because the number of integers separating the first 4 pairs of twin prime numbers are as follows, 0 between (3,5) and (5,7), 3 between (5,7) and (11,13), 3 between (11,13) and (17,19), and 9 between (17,19) and (29,31). 0+3+3+9=15 so a(4)=15.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A001359, A006512. Partial sums of A204099.

s=0; q=2; forprime(p=5, 10^4, if(isprime(p+2), s=s+p-q-3; print1(s", "); q=p)) \\ Jens Kruse Andersen, Aug 17 2014

a(n) = A001359(n+1) - 2 - 3*n. - Robert Israel, Aug 17 2014

A242398 Partial sums of the number of primes separating successive pairs of twin primes.

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 5, 9, 9, 12, 12, 16, 16, 16, 18, 19, 22, 23, 25, 28, 38, 38, 42, 49, 53, 56, 58, 59, 61, 79, 79, 79, 81, 83, 100, 100, 101, 101, 103, 109, 118, 121, 122, 123, 124, 132, 135, 137, 137, 152, 153, 157, 158, 159, 166, 173, 173, 177, 177, 181, 184, 188, 188, 189, 189, 190, 197, 199, 204, 205, 210

Offset: 1

Sam Mathers, Aug 16 2014

nonn

a(n) is the number of primes that are not twin primes greater than the first twin prime pair (3,5) and less than the (n+1)th twin prime pair. All primes, other than two either exist in one of the twin prime pairs or are counted in the sum. Two is not included because it occurs before the first twin prime pair.

			For n=4, a(4)=1. We can get this by writing the first n+1 twin prime pairs and taking the sum of the primes in between them. The pairs are (3,5),(5,7),(11,13),(17,19),(29,31). The only prime between these pairs is 23, thus the answer is one.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Partial sum of A048614.

s=0; forprime(p=5, 10^4, if(isprime(p+2), print1(s", "); s--, s++)) \\ Jens Kruse Andersen, Aug 17 2014

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User: Sam Mathers

A243097 Digit sums of the nontrivial reversal numbers (numbers which are integer multiples of their reversal), excluding palindromes and multiples of 10.

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A242757 Partial sums of the number of integers between successive twin prime pairs.

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PARI

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A242398 Partial sums of the number of primes separating successive pairs of twin primes.

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PARI