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A340112 Prime-acronym numbers: sums of primes which also equal the concatenation of the initial digits of these primes. 1
2, 3, 5, 7, 21, 32, 117, 119, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 169, 171, 172, 173, 175, 177, 179, 187, 211, 212, 213, 215, 217, 218, 221, 231, 232, 233, 235, 237, 251, 253, 271, 272, 273, 275, 277, 281, 311, 319, 321, 322, 323, 325, 327, 329, 331 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..55.

Eric Angelini, Sum of peculiar primes, math-fun mailing list, Dec 24, 2020.

EXAMPLE

Single digit primes trivially satisfy the constraint.

21 is the sum and also concatenation of the initial digits of the primes 2 and 19.

32 is the sum and also concatenation of the initial digits of the primes 3 and 29.

117 is the sum and also concatenation of the initial digits of the primes 19, 19 and 79.

PROG

(PARI) is_A340112(n, d=digits(n), nd=if(vecmin(d), #d))={ /* Check whether n is the sum of primes starting with the digits d[1..nd], respectively. If there's a zero digit, return 0. If there's a single digit left, n must be a prime starting with d[1] */ nd<2 && return(isprime(n) && nd && d[1]==digits(n)[1]); /* else subtract from n a prime p starting with digit d[nd]; check n-p with digits d[1 .. nd-1] */ for( e= !isprime(d[nd]), logint(n, 10), forprime( p=d[nd]*10^e, min(n-vecsum(d[^-1]), (d[nd]+1)*10^e-1), self()(n-p, d[^-1], nd-1) && return(1)))}

CROSSREFS

Cf. A340113 for the subset of primes in this sequence.

Sequence in context: A162948 A024768 A024769 * A085557 A125665 A046034

Adjacent sequences:  A340109 A340110 A340111 * A340113 A340114 A340115

KEYWORD

nonn,base

AUTHOR

Eric Angelini and M. F. Hasler, Dec 28 2020

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)