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A107740 Number of numbers m such that prime(n) = m + (digit sum of m). 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,26

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

Table[p=Prime[n]; c=0; i=1; While[i<p, If[i+Total[IntegerDigits[i]]==p, c=c+1]; i++]; c, {n, 105}]  (* Jayanta Basu, May 03 2013 *)

PROG

(Haskell)

a107740 n = length [() | let p = a000040 n,

                         m <- [max 0 (p - 9 * a055642 p) .. p - 1],

                         a062028 m == p]

-- Reinhard Zumkeller, Sep 27 2014

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

CROSSREFS

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

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

Sequence in context: A027360 A037806 A038082 * A016016 A063059 A214564

Adjacent sequences:  A107737 A107738 A107739 * A107741 A107742 A107743

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, May 23 2005

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)