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A130338 Primes p with no solution x to x=p*digitsum(x). 1
173, 383, 431, 443, 461, 491, 521, 563, 761, 821, 827, 839, 941, 971, 983, 1049, 1481, 1487, 1493, 1499, 1553, 1571, 1601, 1811, 1871, 1931, 2153, 2207, 2477, 2591, 2609, 2753, 3037, 3041, 3083, 3137, 3221, 3251, 3257, 3307, 3329, 3371 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that no number is p times its digit sum.

These may be called the non-Moran primes because no index k exists in A001101 to represent them as A001101(k)/digitsum[A001101(k)]. - R. J. Mathar, Aug 10 2007

LINKS

Table of n, a(n) for n=1..42.

FORMULA

A000040 MINUS {A001101(k)/A007953(A001101(k)): k=1,2,3,4,..}. A003635 INTERSECT A000040. - R. J. Mathar, Aug 10 2007

EXAMPLE

p=5743 is not in the sequence because it can be represented as p=40201/7 (x=40201) or as p=80402/14 (x=80402).

p=7 is not in the sequence because it can be represented as p=21/3 (x=21) or p=42/6 (x=42) or p=63/9 (x=63) or p=84/12 (x=84). In all cases, the denominators are the digit sums of the numerators.

MAPLE

A007953 := proc(n) option remember ; add(j, j=convert(n, base, 10)) ; end: A001101 := proc(p) option remember : local k, digs ; digs := 1; if not isprime(p) then RETURN(-1) ; else while 10^(digs-1)/(9*digs) <= p do for k from max(p, 10^(digs-1)) to 10^digs do if k = p*A007953(k) then RETURN(k) ; fi ; od ; digs := digs+1 ; od: RETURN(-1) ; fi ; end: for n from 1 to 500 do if A001101(ithprime(n)) = -1 then printf("%d, ", ithprime(n)) ; fi : od: # R. J. Mathar, Aug 10 2007

CROSSREFS

Cf. A003635.

Cf. A000040, A001101, A007953, A003635.

Sequence in context: A096703 A060332 A142022 * A275968 A142782 A142250

Adjacent sequences:  A130335 A130336 A130337 * A130339 A130340 A130341

KEYWORD

nonn,base

AUTHOR

Lekraj Beedassy, Aug 07 2007

EXTENSIONS

More terms from R. J. Mathar, Aug 10 2007

STATUS

approved

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Last modified June 5 11:52 EDT 2020. Contains 334840 sequences. (Running on oeis4.)