A107741 -id:A107741 - cp's OEIS frontend

A107740 Number of numbers m such that prime(n) = m + (digit sum of m).

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 0, 1, 1, 0, 1

Offset: 1

Reinhard Zumkeller, May 23 2005

a(A049084(A006378(n))) = 0; a(A049084(A048521(n))) > 0. [Corrected by Reinhard Zumkeller, Sep 27 2014]
a(n) <= 2 for n <= 10^5. Conjecture: sequence is bounded.
I would rather conjecture the opposite. Of course a(n) >= m implies n >= A006064(m), having more than A230857(m) digits, i.e., 14, 25 and 1111111111125 digits of n, for a(n) = 3, 4, 5. - M. F. Hasler, Nov 09 2018

			A000040(26) = 101 = 91 + (9 + 1) = 100 + (1 + 0 + 0): a(26) = # {91, 100} = 2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007953, A000040, A062028, A047791, A107741.

Cf. A006378, A048521, A049084, A055642, A062028.

a107740 n = length [() | let p = a000040 n,
                         m <- [max 0 (p - 9 * a055642 p) .. p - 1],
                         a062028 m == p]
-- Reinhard Zumkeller, Sep 27 2014

Table[p=Prime[n];c=0;i=1;While[iJayanta Basu, May 03 2013 *)

apply( A107740(n)=A230093(prime(n)), [1..150]) \\ M. F. Hasler, Nov 08 2018

a(n) = A230093(prime(n)), i.e.: A107740 = A230093 o A000040. - M. F. Hasler, Nov 08 2018

A048521 Primes expressible as the sum of an integer plus its digit sum.

Original entry on oeis.org

2, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313

Offset: 1

Patrick De Geest, May 15 1999

			a(24) = prime 113 which is 106 + (1+0+6) (or 97 + (9+7)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Cf. A007953, A047791, A048520.
Cf. A006378, A062028, A107741.
Cf. A000040, A107740, A049084.

a048521 n = a048521_list !! (n-1)
a048521_list = map a000040 $ filter ((> 0) . a107740) [1..]
-- Reinhard Zumkeller, Sep 27 2014

t={};Do[p=Prime[n];c=0;i=1;While[iJayanta Basu, May 03 2013 *)
Union[Select[Table[n+Total[IntegerDigits[n]],{n,400}],PrimeQ]] (* Harvey P. Dale, Jul 14 2014 *)

A107740(A049084(a(n))) > 0.

Formula and also offset corrected by Reinhard Zumkeller, Sep 27 2014

cp's OEIS Frontend

A107740 Number of numbers m such that prime(n) = m + (digit sum of m).

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